Question

Genevieve brought $35.75 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. Genevieve had $2.00 left over after buying these items.

Answer 1

The cost of the brush is $2.25, the cost of the sketchbook is $13.50, and the cost of the paint set is $18.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the brush cost is $B, the sketchbook cost is $S, and the paint set cost is $P.

From the problem, we can draw three linear equations in three variables:

The brush was 1/6 as much as the sketchbook:

B = (1/6)S or

6B - S = 0 ...(1)

The sketchbook cost 3/4 the cost of the paint set

S = (3/4)P  or

4S - 3P = 0  ...(2)

The total cost would be:

B+S+P = 35.75 - 2

B+S+P = 33.75  ...(3)

After solving equations (1), (2), and (3) we will get the cost of each item:

B = $2.25

S = $13.50

P = $18

Thus, the cost of the brush is $2.25, the cost of the sketchbook is $13.50, and the cost of the paint set is $18.

Learn more about the linear equation here:

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