Question

Jim and Dwight went to the paint store together. Jim bought 6 cans of paint and 1 paintbrush for $67. Dwight bought 4 cans of the same paint and 3 of the same type of paintbrushes. Dwight's total cost was $54.

a. Write a linear equation to represent Jim's purchase and another to represent Dwight's purchase. Let x represent the cost of a can of paint and y represent the cost of a paint brush.

b. Solve the system of equations using substitution.

c. What was the cost for a can of paint? The cost of a paintbrush?

Answer 1

A can of paint cost $10.50 and a paintbrush costs $4

Explanation:

Using x as the cost of a can of paint and y as the cost of a paint brush, we can write the following system of equations:

6x+y=67

4x+3y=54

We can isolate y in the first equation which gives us:

y=-6x+67

Then we can solve using substitution (substitute -6x+67 for y):

4x+3(-6x+67)=54

4x-18x+201=54

Combine like terms

-14x+201=54

Subtract 201 from both sides

-14x=-147

Divide both sides by -14

x=10.5

Then plug 10.5 back in for x:

y=-6(10.5)+67

y=-63+67

y=4

A can of paint cost $10.50 and a paintbrush costs $4