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