Answer to Question #89881 in Algebra for Ethan

Question

Small pieces were three dollars and large pizzas for five dollars. With the throne, it was necessary to spend $475 for 125 pizzas. How many pieces of each type of purchased?

Answer 1

Assume they bought $x$ small pizzas for $3 and $y$ large pizzas for $5. Then we can write a system of equations:

$$x+y=125,$$ $$3x+5y=475.$$

Solve by subtraction. Multiply both sides of the first equation by 5:

$$5x+5y=125\cdot5.$$ $$3x+5y=475.$$

Subtract the left side of the second from the left side of first, do this for the right sides:

$$5x+5y-3x-5y=625-475.$$

We've got simple equation for $x$:

$$2x=150,\\ x=75.$$

Substitute this to the first one and find $y$:

$$y=125-75=50.$$

75 small pizzas and 50 large ones.