## Fatima brought \$19.50 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 3 as much as the sketchboo

Question

Fatima brought \$19.50 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. Fatima had \$2.00 left over after buying these items. What was the cost of each item?

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1 week 2021-09-12T02:58:01+00:00 1 Answer 0

The brush cost \$1.75, the sketchbook cost \$5.25 and the paint set cost \$10.5

Step-by-step explanation:

Fatima brought \$19.50 to the art supply store which she used to buy a brush, a sketchbook, and a paint set.

Let the cost of the brush be b.

Let the cost of the sketchbook be s.

Let the cost of the paint set be p.

This means that:

b + s + p + 2 = 19.5 __________(1)

The brush was 1/3 as much as the sketchbook:

b = 1/3 * s = s/3 ______ (2)

The sketchbook cost 1/2 the cost of the paint set:

s = 1/2 * p

=> p = 2s________(3)

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

s/3 + s + 2s + 2 = 19.5

=> 10s/3 = 19.5 – 2

10s/3 = 17.5

10s = 17.5 * 3

10s = 52.5

s = \$5.25

Putting this back in (2)

b = 5.25 / 3 = \$1.75

Putting the value of a back in (3)

p = 2 * 5.25 = \$10.5

Therefore, the brush cost \$1.75, the sketchbook cost \$5.25 and the paint set cost \$10.5