Answer to Question #89883 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

We can solve this, using System of Equations

Let`s say that we should buy x small pizzas and y large pizzas.

Now we can create system of equations.

First equation will be

$$3x+5y=475$$

and the second one

$$x+y=125$$

We can solve this one, by substitution :

Step 1:

Solve x+y=125 for x:

$x+y=125\\ x+y+(−y)=125+(−y)\\ x=−y+125$

Step 2:

Substitute −y+125 for x in 3x+5y=475:

$3x+5y=475\\ 3(−y+125)+5y=475\\ 2y+375=475\\ 2y+375+(−375)=475+(−375)\\ 2y=100\\ 2y/2=100/2\\ y=50$

Step 3:

Substitute 50 for y in x=−y+125:

$x=−y+125\\ x=−50+125\\ x=75$

Answer:

We should buy 75 small pizzas and 50 large pizzas.