Andrea brought $54.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was one-sixths as much as the sketchbook, and the sketchbook cost three-fourths the cost of the paint set. Andrea had $1.50 left over after buying these items.

Question

Mathematics

Miles Lutz

24 September, 06:24

Andrea brought $54.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was one-sixths as much as the sketchbook, and the sketchbook cost three-fourths the cost of the paint set. Andrea had $1.50 left over after buying these items.

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Answers (1)

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Gabriella Clark · Answer 1

See explanation below

Step-by-step explanation:

In this case, I'm assuming you want to know the price of all items purchased by Andrea.

Let's gather all the data.

Andrea has initially 54$. From that she got a Brush (B), a sketchbook (S) and a paint set (P). At the end, she has a left over of 1.5$, so she actually spends 52.5$, and our first equation would be:

B + S + P = 52.5 (1)

Now, the B cost 1/6 as the S, and S was 3/4 the paint set, so oru equations here would be:

B = 1/6S (2)

S = 3/4P (3)

Now, according to this we can write the (1) expression in function of (2) and (3).

Replacing (3) in (2):

B = 1/6 (3/4P)

B = 3/24P

B = 1/8P (4)

And replacing (3) and (4) in (1) we have:

1/8P + 3/4P + P = 52.5

From here we can solve for P:

15/8P = 52.5

P = 52.5 * 8 / 15

P = 28.16$

Now we can replace this value to get the Sketchbook, and then, the brush:

S = 3/4 * 28.16

S = 21.12$

B = 1/6 * 21.12

B = 3.52$

These values would be the price of all items.