Dos padres de familia deseaban saber cuáles son los costos de los uniformes escolares que compraron a sus hijos, ya que el primero padre de familia realizó la siguiente compra: 2 pantalones y 2 playeras pagando por ello $820, el segundo padre de familia realizó la siguiente compra, 1 pantalón y 3 playeras pagando por ello $490. Resuelve los siguente cuestionamientos ¿Los padre de familia pagaron al mismo precio cada pantalón y playera? ¿Existe diferencia entre x e y en la ecuación 1 y con respecto a la ecuación 2?

Answer:

a) ¿Pagaron los padres el mismo precio por cada pantalón y camisa?

Sí, los padres pagaron la misma cantidad por cada pantalón y camisa porque,

1 camisa = $ 40

1 pantalón = $ 370

b) ¿Hay alguna diferencia entre xey en la ecuación 1 y con respecto a la ecuación 2?

Sí, hay una diferencia

Step-by-step explanation:

Dos padres querían saber el costo de los uniformes escolares que compraban para sus hijos, ya que

Representemos pantalones = p

camisas = s

Derivamos las 2 ecuaciones

El primer padre hizo la siguiente compra: 2 pantalones y 2 camisas pagando $ 820 por ella

2p + 2s = 820 ........ Ecuación 1

El segundo padre hizo la siguiente compra, 1 pantalón y 3 camisas pagando $ 490.

p + 3s = 490 ....... Ecuación 2

p = 490 - 3 s

Resolvamos el precio de cada pantalón y camisa.

Nosotros sustituimos

2p + 2s = 820

2 (490 - 3 s) + 2 s = 820

980 - 6s + 2s = 820

980 - 820 = 6 segundos - 2 segundos

160 = 4 s

s = 160/4

s = $ 40

Por lo tanto, el costo de cada camisa = $ 40

El costo de los pantalones =

p = 490 - 3 s

p = 490 - 3 (40)

p = 490 - 120

p = $ 370

El costo de cada pantalón = $ 370

Resuelve las siguientes preguntas.

a) ¿Pagaron los padres el mismo precio por cada pantalón y camisa?

Sí, los padres pagaron la misma cantidad por cada pantalón y camisa porque,

1 camisa = $ 40

1 pantalón = $ 370

b) ¿Hay alguna diferencia entre xey en la ecuación 1 y con respecto a la ecuación 2?

Sí, hay una diferencia

Planteando y resolviendo un sistema de ecuaciones, veremos que cada playera cuesta $40 y cada pantalon cuesta $370.

Definamos:

Por la información dada, tenemos que:

2*x + 2*y = $820

1*x + 3*y = $490

Primero respondamos las preguntas:

Notar que ambas preguntas basicamente preguntan la misma cosa:

¿Existe diferencia entre x e y en la ecuación 1 y con respecto a la ecuación 2?

Es realmente imposible saber la respuesta, pero debemos asumir que no, dado que si x e y representan diferentes cosas en cada ecuación, entonces las variables no estan definidas, y el problema es imposible de resolver.

Así que asumimos que los precios son los mismos.

con esto en mente, podemos resolver el sistema:

2*x + 2*y = $820

1*x + 3*y = $490

Primero, aislamos una variable en una ecuación, en este caso voy a aislar x en la segunda:

x = $490 - 3*y

Reemplazamos eso en la primera:

2*($490 - 3*y) + 2*y = $820

$980 - 4*y = $820

$980 - $820 = 4*y

$160/4 = y  = $40

Es decir, el precio de cada playera es $40.

Mientras que:

x = $490 - 3*$40 = $370

Cada pantalon cuesta $370

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