Question

Audrina brought $35.25 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Audrina had $1.50 leftover after buying these items. What was the cost of each item?

Answer 1

Answer: paint set costs $18

sketchbook costs $13.5

Brush costs $2.25

Explanation:

Let x represent the cost of the paint set.

The sketchbook cost 3/4 the cost of the paint set. It means that the cost of the sketchbook is

3/4 × x = 3x/4

The brush was 1/6 as much as the sketchbook. It means that the cost of the brush is

1/6 × 3x/4 = 3x/24 = x/8

Audrina brought $35.25 to the art supply store. If Audrina had $1.50 leftover after buying these items, it means that the amount spent on the items is

35.25 - 1.5 = 33.75

Therefore,

x + 3x/4 + x/8 = 33.75

Multiplying through by 8, it becomes

8x + 6x + x = 270

15x = 270

x = 270/15

x = 18

The cost of the sketchbook is

(3 × 18)/4 = 13.5

The cost of the brush is

1/8 × 18 = 2.25

Answer 2

The brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.

Explanation:

Givens

• Audrian has $35.25
• The brush was 1/6 as much as the sketchbook.
• The sketchbook cost 3/4 the cost of the paint set.
• Audrina had $1.50 leftover.
• She bough a brush, a sketchbook and a paint set.

Based on the given information, we can form the following equations.

`b=(1)/(2)s`

Where
`b` is the brush and
`s` is the sketchbook.

`s=(3)/(4)p`

Where
`p` is paint set.

Now, the sum of all three items would give $1.50 of leftover.

`p+b+s=35.25-1.50`

Replacing expressions, we have

`p+(1)/(2)s+(3)/(4)p=30.75\\ (7)/(4)p +(1)/(2)((3)/(4) p)=30.75\\(7)/(4)p+(3)/(8)p=30.75\\ (56p+12p)/(32)=30.75\\ 68p=984\\p=(984)/(68)=14.50`

Then, we use this value to find the other variables

`s=(3)/(4)(14.50)=10.88`

`b=(1)/(2)(10.88)=5.44`

Therefore, the brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.