Keiko brought $29.50 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 3 as much as the sketchbook, and the sketchbook cost 1 2 the cost of the paint set. Keiko had $4.50 left over after buying these items. What was the cost of each item? Solve on paper. Then check your work on Zearn.

The brush costs $2.50, the sketchbook costs $7.50 and the paint set costs $15

Step-by-step explanation:

Let the cost of a brush be b.

Let the cost of a sketchbook be s.

Let the cost of a paint set be p.

Keiko brought $29.50 to the art supply store.

She bought one of each of the following: a brush, a sketchbook, and a paint set.

The brush was 1/3 as much as the sketchbook. This means that:

b = 1/3 * s = s/3 (1)

The sketchbook cost 1/2 the cost of the paint set. This means that:

s = 1/2 * p = p/2

=> p = 2s (2)

Keiko had $4.50 left over after buying these items.

This implies that the leftover plus the prices of all the items she bought will equal the initial money she brought to the store:

b + s + p + 4.5 = 29.50 (3)

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

s/3 + s + 2s + 4.5 = 29.5

10s/3 = 29.5 - 4.5 = 25

=> s = (25 * 3) / 10

s = $7.50

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

b = 7.5 / 3 = $2.50

and

p = 2 * 7.50 = $15

Therefore, the brush costs $2.50, the sketchbook costs $7.50 and the paint set costs $15.

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step-by-step explanation: