Question

Monica built a porch that contained 2 different colors of bricks to create a pattern. She purchased the red bricks for $7 each and the gray bricks for $4 each. Write a system to find out how many red bricks Monica purchased if she spent $193 on 40 bricks?

a. What is the system that models this situation?
Equation #1:
Equation #2:

b. How many red bricks did Monica purchase?

Answer 1

a.

`\left\{\begin{array}{l}x+y=40\\ \\7x+4y=193\end{array}\right.`

b. 11 red bricks

Explanation:

Let x be the number of red bricks and y be the number of grey bricks.

1. Monica purchased 40 bricks, so

`x+y=40`

2. If she purchased the red bricks for $7 each, then x red bricks cost $7x. If the gray bricks are for $4 each, then y bricks cost $4y. In total, all bricks cost $(7x + 4y) that is $193. Hence,

`7x+4y=193`

a. The system of two equations is

`\left\{\begin{array}{l}x+y=40\\ \\7x+4y=193\end{array}\right.`

b. From the first equation:

`y=40-x`

Substitute it into the second equation:

`7(40-y)+4y=193\\ \\280-7y+4y=193\\ \\-7y+4y=193-280\\ \\-3y=-87\\ \\3y=87\\ \\y=29\\ \\x=40-29=11`

Monica purshased 11 red bricks and 29 grey bricks.