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.

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