Question

Tomas brought $32.00 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 4 as much as the sketchbook, and the sketchbook cost 2 3 the cost of the paint set. Tomas had $4.50 left over after buying these items.

Answer 1

I want to delete my answer because the one already answered is correct.

Answer 2

The price of the sketchbook is $10, the price of the brush is $2.5 and the price of the paint set is $15.

Explanation:

Let the price of the brush be b.

Let the price of the sketchbook be s.

Let the price of the paint set be p.

The brush was 1/4 as much as the sketchbook. This means that:

b = 1/4 * s = s/4_______________(1)

The sketchbook was 2/3 the cost of the paint set. This means that:

s = 2/3 * p

=> p = 3s/2 __________________(2)

Initially, he had $32.00 and after buying all the items, he had $4.50 left with him. This means that:

b + s + p + 4.50 = 32.00 ___________(3)

Put (1) and (2) in (3):

=> s/4 + s + 3s/2 + 4.50 = 32.00

Collect like terms and simplify:

11s/4 = 32.00 - 4.50 = 27.5

=> s = (27.5 * 4) / 11

s = $10

Put this back in (1) and (2):

b = 10 / 4 = $2.5

and

p = (3 * 10) / 2 = $15

The price of the sketchbook is $10, the price of the brush is $2.5 and the price of the paint set is $15.