Alex y felipe son carpinteros. la materia prima necesaria para hacer un mueble grande les cuesta $500 y para un mueble pequeño $300. si tienen $57000 y quieren hacer 150 muebles. ¿ cuantos muebles de cada tamaño podrán hacer? hay amor ue resolver mediante sostemas de ecuaciones

Large furniture = 110 and Small furniture = 40

Step-by-step explanation:

Let, the number of pieces of large furniture = x and the number of small furniture = y.

As, it is given that Alex makes 150 pieces of the furniture.

We get the relation x + y = 150.

Moreover, the cost to make large furniture is $500 and the cost to make small furniture is $300.

Since, they have $57,000 as the total amount.

Thus, we get, 500x + 300y = 57000 i.e. 5x + 3y = 570.

Hence, we get the system of equations as,

5x + 3y = 570

x + y = 150

Now, we will solve these equations.

As, x + y = 150 ⇒ x = 150 - y

So, 5x + 3y = 570 ⇒ 5(150-y) + 3y = 570 ⇒ 650 - 5y + 3y = 570 ⇒ -2y = -80 ⇒ y = 40

Thus,  x = 150 - 40 = 110 ⇒ x = 110

Hence, the number of large furniture can be made is 110 and the number of small furniture can be made is 40.