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

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    2021-09-12T02:59:45+00:00

    Answer:

    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.

    After buying them, she had $2.00 left over.

    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

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