Answer:
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.
