Answer :
Answer:
The brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.
Step-by-step 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.
[tex]b=\frac{1}{2}s[/tex]
Where [tex]b[/tex] is the brush and [tex]s[/tex] is the sketchbook.
[tex]s=\frac{3}{4}p[/tex]
Where [tex]p[/tex] is paint set.
Now, the sum of all three items would give $1.50 of leftover.
[tex]p+b+s=35.25-1.50[/tex]
Replacing expressions, we have
[tex]p+\frac{1}{2}s+\frac{3}{4}p=30.75\\ \frac{7}{4}p +\frac{1}{2}(\frac{3}{4} p)=30.75\\\frac{7}{4}p+\frac{3}{8}p=30.75\\ \frac{56p+12p}{32}=30.75\\ 68p=984\\p=\frac{984}{68}=14.50[/tex]
Then, we use this value to find the other variables
[tex]s=\frac{3}{4}(14.50)=10.88[/tex]
[tex]b=\frac{1}{2}(10.88)=5.44[/tex]
Therefore, the brush cost $5.44, the sketchbook cost 10.88 and the paint set cost 14.50, approximately.
Answer: paint set costs $18
sketchbook costs $13.5
Brush costs $2.25
Step-by-step 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