Monica built a porch that contained 2 different colors of bricks to create a pattern. She purchased the red bricks for $7 each a

Question

3 years ago

9

Monica built a porch that contained 2 different colors of bricks to create a pattern. She purchased the red bricks for $7 each a

nd the gray bricks for $4 each.
Write a system to find how many red bricks did Monica purchase if she spent $193 on 40 bricks?

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

How many red bricks did Monica purchase?

Mathematics

1 answer:

ahrayia [7] · Answer 1 · 2021-12-11T14:50:48+03:00

Equation #1: x+y=40

Equation #2: 7x+4y=193

Monica bought 11 red bricks.

Step-by-step explanation:

Given,

Cost of one red brick = $7

Cost of one gray brick = $4

Total spent on bricks = $193

Total bricks bought = 40

Let,

x represents the number of red bricks bought.

y represents the number of gray bricks bought.

What is the system that models this situation?

Equation #1: x+y=40

Equation #2: 7x+4y=193

How many red bricks did Monica purchase?

Multiplying Eqn 1 by 4

$4(x+y=40)\\4x+4y=160\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(7x+4y)-(4x+4y)=193-160\\7x+4y-4x-4y=33\\3x=33$

Dividing both sides by 3

$\frac{3x}{3}=\frac{33}{3}\\x=11$

Monica bought 11 red bricks.

Keywords: linear equation, elimination method

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