Answer:
The cost of paint = $19.50¢
The cost of sketchbook = $9.75¢
The cost of the brush = $3.25¢
Step-by-step explanation:
Let us denote the price or cost of the paint set by k. According to the question, the sketchbook costs 1/2 the cost of the paint.
This means that the sketchbook's cost is =
1/2 × k = k/2
Again, the brush was 1/3 as much as the sketchbook. This means that the brush's cost=
1/3 of k/2 = 1/3 × k/2 = k/6 (The cost of a brush)
The total cost of the items purchased is =
k+(k/2)+(k/6).... Using LCM to find a common denominator= (6k+3k+k)/6 = 10k/6 = 5k/3
We were told that $37 was taken to the store and after the purchase of these items, Paul had a balance of $4.50.
This means that:
$37 - (5k/3) = $4.50
Using LCM to find a common denominator for the left side of the equation:
(111-5k)/3 = 4.50
111-5k = 13.50
5k = 111-13.50
5k = 97.50
k = $19.50¢
Therefore, the cost of the paint set is $19.50¢
The cost of the sketchbook will now be half of the cost of the paint = 1/2 of 19.50 = 1/2 × 19.50 = $9.75¢
The cost of the brush will now be a third of the cost of the sketchbook
= 1/3 of 9.75 = 1/3 × 9.75 = $3.25¢
