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19 December, 14:52

Madison brought $42.50 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. Madison had $4.00 left over after buying these items.

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  1. 19 December, 15:19
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    Amount spent on each item is;

    brush = $3.50

    sketchbook = $14.00

    paint set = $21.00

    Completed question:

    Madison brought $42.50 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. Madison had $4.00 left over after buying these items. How much is each item.

    Step-by-step explanation:

    Let x, y and z represent the price of brush, sketchbook and paint set respectively.

    The brush was 1/4 as much as the sketchbook,

    x = 1/4 * y

    y = 4x ... 1

    the sketchbook cost 2/3 the cost of the paint set

    y = 2/3 * z

    3y = 2z

    z = 3y/2

    Substituting equation 1

    z = 3 (4x) / 2 = 6x

    z = 6x ... 2

    Total amount spent = amount he brought - amount he left with (remainder)

    = $42.50 - $4.00

    = $38.50

    Total amount spent = x+y+z = $38.50

    x+y+z = 38.50

    Substituting equation 1 and 2

    x + 4x + 6x = 38.50

    11x = 38.50

    x = 38.50/11

    x = 3.5

    y = 4x = 4 (3.5) = 14

    z = 6x = 6 (3.5) = 21

    Amount spent on each item is;

    brush = $3.50

    sketchbook = $14.00

    paint set = $21.00
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