Matt brought $40.50 to the art supply store. He bought a brush, a sketchbook, and paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Matt had $3.00 left over after buying these items.

cost of paint set = $20

cost of the sketch box = 3/4 × 20 = $15

cost of the brush = 3/24 × 20 = 60/24 = $2.5

Step-by-step explanation:

The total amount Matt brought to the art supply store is $40.50.  He bought a brush, a sketchbook and a paint set. This means he bought 3 items. The question wants us to find the price of each item.

Let

price of paint set =  b

price of the sketchbook = 3/4b

price of the brush = 1/6 × 3/4 b = 3/24 b

adding the sum

b + 3/4 b + 3/24 b + 3 = 40.50

b + 3/4 b + 1/8 b + 3 = 40.50

collect like terms

8b + 6b + b/8 = 40.50 - 3

15b/8 = 37.5

cross multiply

15b = 300

divide both sides by 15

b = 300/15

b = $20

cost of paint set = $20

cost of the sketch box = 3/4 × 20 = $15

cost of the brush = 3/24 × 20 = 60/24 = $2.5