Sara brought $37.25 to the art supply store. She 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. Sara had $1.50 left over after buying these items. What was the cost of each item?

The cost of the brush is $3.25, the cost of the sketchbook is $13, and the cost of the paint set is $19.50

Step-by-step explanation:

Let m represent the cost of the brush.

Since the brush was 1/4 as much as the sketchbook, the sketchbook costs 4m

Since the sketchbook cost 2/3 the cost of the paint set, the paint set costs 4m (3/2) = 6m

Since she bought a brush, a sketchbook, and a paint set, the money she spent can represented as:

m + 4m + 6m = 11m

Since she brought $37.25 and had $1.50 left over, she spent:

37.25 - 1.50 = 35.75

→ 11m = 35.75

→ m = 3.25

The cost of the brush → m = 3.25

The cost of the sketchbook → 4m = 4 (3.25) = 13

The cost of the paint set → 6m = 6 (3.25) = 19.50