137:@0.942817:0.963886:0.974741:0.963886:0.974741:0.945448:0.942817:0.945448:0.000000:0.000000:0.000000
Ejemplo:@0.095800:0.131225:0.153160:0.131225:0.153160:0.116112:0.095800:0.116112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Julián va a comprar una maleta que cuesta $ 150. Para pagar solo tiene billetes de :@0.095800:0.155264:0.698237:0.155264:0.698237:0.139594:0.095800:0.139594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
$ 10 y $ 5. ¿Cuántos billetes de cada tipo necesita para comprar la maleta?:@0.095800:0.171860:0.637164:0.171860:0.637164:0.156191:0.095800:0.156191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.095800:0.193761:0.156461:0.193761:0.156461:0.178649:0.095800:0.178649:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identificamos las variables::@0.095800:0.217800:0.290136:0.217800:0.290136:0.202130:0.095800:0.202130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.095800:0.241519:0.103263:0.241519:0.103263:0.225157:0.095800:0.225157:0.000000
: billetes de $ 10,  : billetes de $ 5.:@0.103263:0.241519:0.347115:0.241519:0.347115:0.225849:0.103263:0.225849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.227961:0.241519:0.235443:0.241519:0.235443:0.225157:0.227961:0.225157:0.000000
La ecuación formada es: 10  + 5  = 150. Dividimos la ecuación para 5 y obtenemos :@0.095800:0.265238:0.698069:0.265238:0.698069:0.249568:0.095800:0.249568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.292182:0.265238:0.299645:0.265238:0.299645:0.248876:0.292182:0.248876:0.000000
y:@0.326586:0.265238:0.334068:0.265238:0.334068:0.248876:0.326586:0.248876:0.000000
una ecuación equivalente: 2  +   = 30:@0.095800:0.281834:0.372729:0.281834:0.372729:0.266164:0.095800:0.266164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.301690:0.281834:0.309154:0.281834:0.309154:0.265473:0.301690:0.265473:0.000000
y:@0.328208:0.281834:0.335689:0.281834:0.335689:0.265473:0.328208:0.265473:0.000000
Para encontrar los puntos de la recta solución, despejamos  .:@0.095800:0.305553:0.540234:0.305553:0.540234:0.289883:0.095800:0.289883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.529546:0.305553:0.537028:0.305553:0.537028:0.289192:0.529546:0.289192:0.000000
y:@0.095800:0.329272:0.103282:0.329272:0.103282:0.312911:0.095800:0.312911:0.000000
 = 30 – 2:@0.103282:0.329272:0.166599:0.329272:0.166599:0.313602:0.103282:0.313602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.166599:0.329272:0.174062:0.329272:0.174062:0.312911:0.166599:0.312911:0.000000
Asignamos diferentes valores a  .:@0.095800:0.352991:0.336480:0.352991:0.336480:0.337321:0.095800:0.337321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.325810:0.352991:0.333274:0.352991:0.333274:0.336630:0.325810:0.336630:0.000000
x:@0.115875:0.382257:0.124218:0.382257:0.124218:0.366704:0.115875:0.366704:0.000000
y :@0.172197:0.382257:0.183605:0.382257:0.183605:0.366704:0.172197:0.366704:0.000000:0.000000
= 30 – 2:@0.183605:0.382257:0.240010:0.382257:0.240010:0.366679:0.183605:0.366679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.240010:0.382257:0.248353:0.382257:0.248353:0.366704:0.240010:0.366704:0.000000
y:@0.296332:0.382257:0.304658:0.382257:0.304658:0.366704:0.296332:0.366704:0.000000
3:@0.115959:0.412231:0.124134:0.412231:0.124134:0.397986:0.115959:0.397986:0.000000
y :@0.169885:0.412231:0.179702:0.412231:0.179702:0.397357:0.169885:0.397357:0.000000:0.000000
= 30 – 2(3):@0.179702:0.412231:0.250648:0.412231:0.250648:0.397986:0.179702:0.397986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
24:@0.292311:0.412231:0.308662:0.412231:0.308662:0.397986:0.292311:0.397986:0.000000:0.000000
5:@0.115942:0.443048:0.124117:0.443048:0.124117:0.428803:0.115942:0.428803:0.000000
y :@0.169868:0.443048:0.179685:0.443048:0.179685:0.428174:0.169868:0.428174:0.000000:0.000000
= 30 – 2(5):@0.179685:0.443048:0.250631:0.443048:0.250631:0.428803:0.179685:0.428803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
20:@0.292295:0.443048:0.308645:0.443048:0.308645:0.428803:0.292295:0.428803:0.000000:0.000000
7:@0.115925:0.473864:0.124101:0.473864:0.124101:0.459619:0.115925:0.459619:0.000000
y :@0.169851:0.473864:0.179668:0.473864:0.179668:0.458990:0.169851:0.458990:0.000000:0.000000
= 30 – 2(7):@0.179668:0.473864:0.250615:0.473864:0.250615:0.459619:0.179668:0.459619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
16:@0.292278:0.473864:0.308628:0.473864:0.308628:0.459619:0.292278:0.459619:0.000000:0.000000
10:@0.111821:0.504681:0.128171:0.504681:0.128171:0.490435:0.111821:0.490435:0.000000:0.000000
y = 30 – 2(10):@0.165144:0.504681:0.255305:0.504681:0.255305:0.490435:0.165144:0.490435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10:@0.292278:0.504681:0.308628:0.504681:0.308628:0.490435:0.292278:0.490435:0.000000:0.000000
De las soluciones obtenidas se consideran solo las que satisfacen la ecuación del :@0.095800:0.539889:0.698244:0.539889:0.698244:0.524219:0.095800:0.524219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problema: 10  + 5  = 150:@0.095800:0.556485:0.281293:0.556485:0.281293:0.540815:0.095800:0.540815:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.192711:0.556665:0.199861:0.556665:0.199861:0.540912:0.192711:0.540912:0.000000
y:@0.227908:0.556665:0.235261:0.556665:0.235261:0.540912:0.227908:0.540912:0.000000
Tabulando los datos que sí satisfacen la ecuación, tenemos la siguiente tabla de :@0.095800:0.580204:0.681644:0.580204:0.681644:0.564534:0.095800:0.564534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores::@0.095800:0.596801:0.150457:0.596801:0.150457:0.581131:0.095800:0.581131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 596461766 :@0.920815:0.265563:0.920815:0.189945:0.909426:0.189945:0.909426:0.265563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Su representación gráfica es::@0.406789:0.620145:0.615444:0.620145:0.615444:0.604475:0.406789:0.604475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.135429:0.630376:0.143772:0.630376:0.143772:0.614823:0.135429:0.614823:0.000000
y:@0.220916:0.630376:0.229242:0.630376:0.229242:0.614823:0.220916:0.614823:0.000000
Puntos:@0.284525:0.630376:0.336575:0.630376:0.336575:0.614798:0.284525:0.614798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.135513:0.656791:0.143688:0.656791:0.143688:0.642546:0.135513:0.642546:0.000000
24:@0.216896:0.656791:0.233246:0.656791:0.233246:0.642546:0.216896:0.642546:0.000000:0.000000
A (3, 24):@0.283822:0.656791:0.337279:0.656791:0.337279:0.642546:0.283822:0.642546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.135513:0.680479:0.143688:0.680479:0.143688:0.666234:0.135513:0.666234:0.000000
20:@0.216896:0.680479:0.233246:0.680479:0.233246:0.666234:0.216896:0.666234:0.000000:0.000000
B (5, 20):@0.284492:0.680479:0.336608:0.680479:0.336608:0.666234:0.284492:0.666234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7:@0.135513:0.704167:0.143688:0.704167:0.143688:0.689921:0.135513:0.689921:0.000000
16:@0.216896:0.704167:0.233246:0.704167:0.233246:0.689921:0.216896:0.689921:0.000000:0.000000
C (7, 16):@0.283939:0.704167:0.337145:0.704167:0.337145:0.689921:0.283939:0.689921:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10:@0.131408:0.727854:0.147759:0.727854:0.147759:0.713609:0.131408:0.713609:0.000000:0.000000
10:@0.216963:0.727854:0.233146:0.727854:0.233146:0.713609:0.216963:0.713609:0.000000:0.000000
D (10, 10):@0.279198:0.727854:0.341869:0.727854:0.341869:0.713609:0.279198:0.713609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15:@0.131408:0.751542:0.147759:0.751542:0.147759:0.737296:0.131408:0.737296:0.000000:0.000000
0:@0.220967:0.751542:0.229142:0.751542:0.229142:0.737296:0.220967:0.737296:0.000000
E (15, 0):@0.284793:0.751542:0.336257:0.751542:0.336257:0.737296:0.284793:0.737296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.534940:0.774726:0.539688:0.774726:0.539688:0.766074:0.534940:0.766074:0.000000
10:@0.583458:0.774726:0.592953:0.774726:0.592953:0.766074:0.583458:0.766074:0.000000:0.000000
15:@0.634349:0.774726:0.643844:0.774726:0.643844:0.766074:0.634349:0.766074:0.000000:0.000000
-5:@0.431660:0.774726:0.439307:0.774726:0.439307:0.766074:0.431660:0.766074:0.000000:0.000000
0:@0.488408:0.773266:0.493156:0.773266:0.493156:0.764613:0.488408:0.764613:0.000000
0:@0.479633:0.764993:0.484380:0.764993:0.484380:0.756340:0.479633:0.756340:0.000000
5:@0.477602:0.744220:0.482349:0.744220:0.482349:0.735568:0.477602:0.735568:0.000000
10:@0.473010:0.719154:0.482505:0.719154:0.482505:0.710501:0.473010:0.710501:0.000000:0.000000
15:@0.473058:0.694576:0.482554:0.694576:0.482554:0.685924:0.473058:0.685924:0.000000:0.000000
20:@0.473058:0.669707:0.482554:0.669707:0.482554:0.661054:0.473058:0.661054:0.000000:0.000000
25:@0.473029:0.644670:0.482524:0.644670:0.482524:0.636017:0.473029:0.636017:0.000000:0.000000
y:@0.474189:0.634480:0.478470:0.634480:0.478470:0.625828:0.474189:0.625828:0.000000
x:@0.680431:0.774726:0.684605:0.774726:0.684605:0.766074:0.680431:0.766074:0.000000
A:@0.521059:0.647883:0.529990:0.647883:0.529990:0.634718:0.521059:0.634718:0.000000
B:@0.541227:0.668189:0.549136:0.668189:0.549136:0.655024:0.541227:0.655024:0.000000
C:@0.562547:0.689349:0.571011:0.689349:0.571011:0.676184:0.562547:0.676184:0.000000
D:@0.592842:0.717945:0.602561:0.717945:0.602561:0.704781:0.592842:0.704781:0.000000
E:@0.641174:0.765906:0.648354:0.765906:0.648354:0.752741:0.641174:0.752741:0.000000
Mediante la gráfica trazada, se pueden dar diversas respuestas al problema. Por :@0.095800:0.801728:0.698163:0.801728:0.698163:0.786058:0.095800:0.786058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, para pagar $ 150.:@0.095800:0.818324:0.289491:0.818324:0.289491:0.802655:0.095800:0.802655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.095800:0.842043:0.105567:0.842043:0.105567:0.824908:0.095800:0.824908:0.000000:0.000000
Se necesitan 3 billetes de $ 10 y 24 de $ 5.:@0.119535:0.842043:0.417565:0.842043:0.417565:0.826374:0.119535:0.826374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.095800:0.865762:0.105567:0.865762:0.105567:0.848627:0.095800:0.848627:0.000000:0.000000
Se necesitan 5 billetes de $ 10 y 20 billetes de $ 5.:@0.119535:0.865762:0.472111:0.865762:0.472111:0.850093:0.119535:0.850093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.095800:0.889481:0.105567:0.889481:0.105567:0.872346:0.095800:0.872346:0.000000:0.000000
Se necesitan 7 billetes de $ 10 y $ 16 billetes de $ 5.:@0.119535:0.889481:0.484769:0.889481:0.484769:0.873812:0.119535:0.873812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.095800:0.913200:0.105567:0.913200:0.105567:0.896065:0.095800:0.896065:0.000000:0.000000
Se necesitan 10 billetes de $ 10 y $ 10 billetes de $ 5.:@0.119535:0.913200:0.493577:0.913200:0.493577:0.897531:0.119535:0.897531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuando trabajes en :@0.733359:0.777950:0.866942:0.777950:0.866942:0.763705:0.733359:0.763705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
grupo, toma la iniciativa :@0.733359:0.793038:0.896510:0.793038:0.896510:0.778792:0.733359:0.778792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y manifiesta tus puntos :@0.733359:0.808125:0.892151:0.808125:0.892151:0.793880:0.733359:0.793880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de vista en la resolución :@0.733359:0.823213:0.896659:0.823213:0.896659:0.808968:0.733359:0.808968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de problemas para :@0.733359:0.838300:0.862419:0.838300:0.862419:0.824055:0.733359:0.824055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llegar a soluciones :@0.733359:0.853388:0.859705:0.853388:0.859705:0.839143:0.733359:0.839143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
efectivas.:@0.733359:0.868476:0.794235:0.868476:0.794235:0.854230:0.733359:0.854230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Emite:@0.733359:0.890692:0.773330:0.890692:0.773330:0.875579:0.733359:0.875579:0.000000:0.000000:0.000000:0.000000:0.000000
 tu opinión en :@0.773330:0.890692:0.871214:0.890692:0.871214:0.876447:0.773330:0.876447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
clase.:@0.733359:0.905780:0.769108:0.905780:0.769108:0.891535:0.733359:0.891535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia  :@0.763694:0.740965:0.874721:0.740965:0.874721:0.724065:0.763694:0.724065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.763694:0.754796:0.886312:0.754796:0.886312:0.737895:0.763694:0.737895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 310100930:@0.919947:0.569952:0.919947:0.495986:0.908559:0.495986:0.908559:0.569952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Existen calculadoras, :@0.733044:0.363747:0.873008:0.363747:0.873008:0.349502:0.733044:0.349502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como la fx 9860 GSD :@0.733044:0.378835:0.874903:0.378835:0.874903:0.364590:0.733044:0.364590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que te permiten :@0.733044:0.393922:0.845183:0.393922:0.845183:0.379677:0.733044:0.379677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resolver ecuaciones :@0.733044:0.409010:0.867834:0.409010:0.867834:0.394765:0.733044:0.394765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lineales con dos :@0.733044:0.424098:0.843375:0.424098:0.843375:0.409852:0.733044:0.409852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
incógnitas, calculando :@0.733044:0.439185:0.885625:0.439185:0.885625:0.424940:0.733044:0.424940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su tabla de valores y :@0.733044:0.454273:0.871099:0.454273:0.871099:0.440028:0.733044:0.440028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mostrando la gráfica de :@0.733044:0.469361:0.894435:0.469361:0.894435:0.455115:0.733044:0.455115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la ecuación.:@0.733044:0.484448:0.811747:0.484448:0.811747:0.470203:0.733044:0.470203:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia digital:@0.747853:0.338117:0.898755:0.338117:0.898755:0.321217:0.747853:0.321217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga  resume:@0.732687:0.590771:0.847642:0.590771:0.847642:0.575658:0.732687:0.575658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y:@0.781118:0.590771:0.792158:0.590771:0.792158:0.576525:0.781118:0.576525:0.000000:0.000000
 en :@0.847642:0.590771:0.872084:0.590771:0.872084:0.576525:0.847642:0.576525:0.000000:0.000000:0.000000:0.000000
el cuaderno: ¿cómo :@0.732687:0.605858:0.864997:0.605858:0.864997:0.591613:0.732687:0.591613:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se resuelven las :@0.732687:0.620946:0.837224:0.620946:0.837224:0.606701:0.732687:0.606701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuaciones lineales con :@0.732687:0.636033:0.892234:0.636033:0.892234:0.621788:0.732687:0.621788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos incógnitas en una :@0.732687:0.651121:0.883576:0.651121:0.883576:0.636876:0.732687:0.636876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
calculadora que realiza :@0.732687:0.666209:0.888416:0.666209:0.888416:0.651963:0.732687:0.651963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esta operación?:@0.732687:0.681296:0.837591:0.681296:0.837591:0.667051:0.732687:0.667051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000