linear equations

Question

Steve Fletcher wants to design a walkway to his house using two different kinds of paving bricks. He fins the job will require 380 bricks. The home improvement store sells two kinds of paving bricks that will work together, a red brick variety that sells for $5.00 per unit, and a cement brick that sells for $3.00 per unit. How many of each type of brick should he buy if he has budgeted $1500 for the project?

Answer 1

red brick = x

cement brick = y

Create two equations based on number of bricks and cost:

x + y = 380   and 5x + 3y = 1500

Use the first equation to solve for x so that you can substitute it into the second equation:

x + y - y = 380 - y

x = 380 - y

 

5x + 3y = 1500

5(380 - y) + 3y = 1500

1900 - 5y + 3y = 1500

1900 - 2y = 1500

 -1900       -1900

-2y = -400

÷(-2)  ÷(-2)

y = 200         there are 200 cement bricks

 

Now substitute that answer in an equation to find the number of red bricks

x = 380 - y

x = 380 - 200

x = 180          there are 180 red bricks

 

 

Have a great day!

Colossians 3:23