Question

Paul brought $37 to the art supply store. He bought a brush a sketchbook and a paint set. The brush was 1/3 as much as the strechbook and the sketchbook cost 1/2 the cost of the paint set. Paul had $4.50 left over after buying these items what is the cost of each item?

Answer 1

Answer: B = $ 3.25

S = $ 9.75

P = $ 19.5

Step-by-step explanation: Please find the attached file for the solution

Answer 2

Answer:

The cost of paint = $19.50¢

The cost of sketchbook = $9.75¢

The cost of the brush = $3.25¢

Step-by-step explanation:

Let us denote the price or cost of the paint set by k. According to the question, the sketchbook costs 1/2 the cost of the paint.

This means that the sketchbook's cost is =

1/2 × k = k/2

Again, the brush was 1/3 as much as the sketchbook. This means that the brush's cost=

1/3 of k/2 = 1/3 × k/2 = k/6 (The cost of a brush)

The total cost of the items purchased is =

k+(k/2)+(k/6).... Using LCM to find a common denominator= (6k+3k+k)/6 = 10k/6 = 5k/3

We were told that $37 was taken to the store and after the purchase of these items, Paul had a balance of $4.50.

This means that:

$37 - (5k/3) = $4.50

Using LCM to find a common denominator for the left side of the equation:

(111-5k)/3 = 4.50

111-5k = 13.50

5k = 111-13.50

5k = 97.50

k = $19.50¢

Therefore, the cost of the paint set is $19.50¢

The cost of the sketchbook will now be half of the cost of the paint = 1/2 of 19.50 = 1/2 × 19.50 = $9.75¢

The cost of the brush will now be a third of the cost of the sketchbook

= 1/3 of 9.75 = 1/3 × 9.75 = $3.25¢