Question

22. Tad and Timothy went to the paint store together. Tad bought 6 cans of paint

and 1 paint brush for $67. Timothy bought 4 cans of the same paint and 3 of
the same type of paint brushes. Timothy’s total cost was $54.
(Let x represent the cost of a can of paint and y represent the cost of a paint brush.)

a. Solve the system of linear equations using the substitution method.
b. What was the cost for a can of paint?
c. The cost of a paint brush?

Answer 1

Can of Paint = $10.50

Paint Brush = $4

Explanation:

P and B are paintbrushes and brushes. x and y are the numbers of P and B, respectively.

x y

P B $

Tad 6 1 67

Tim 4 3 54

We can form two equations from the above table:

For Tad: 6x + 1y = 67 [the numbers of paint and brushes times their costs, x and y, is the total Tad paid, $67]

For Tim: 4x + 3y = 54 {Same approach]

We have two equations and two unknowns, so let's rearrange on one of the equations to isolate one of the two variables, and then use that in the other equation. I'll pick the first and rearrange it for y:

6x + 1y = 67

y = 67-6x

Now use this value of y in the second equation:

4x + 3y = 54

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

4x + 201 -18x = 54

-14x = - 147

x = $10.5 The price of a can of paint is $10.50

Now use this value of x in either equation and solve for y:

6x + 1y = 67

y = 67-6*(10.5)

y = 67-63

y = $4 The price for a brush is $4

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See if these values work:

Did Tad pay the correct amount?:

6x + 1y = 67

6($10.5) + 1($4) = $67 ??

$63 + $4 = $67 YES

How about for Timothy?

4x + 3y = 54

4($10.5) + 3($4) = 54?

$42 + $12 = $54

The values are correct.