Alex won a gift card worth $96.00 for winning a design competition. She decided to spend her winnings on sketchbooks and paint sets. Each sketchbook (x) cost $12.00, while each paint set (y) cost $15.00. Which of the following combinations of sketchbooks and paint sets can Alex purchase assuming she spends her entire gift card.

Question

A. 1 sketchbook and 4 paint sets
B. 3 sketchbooks and 4 paint sets
C. 4 sketchbooks and 3 paint sets
D. 2 sketchbooks and 5 paint sets

Answer 1

To determine which combinations of sketchbooks and paint sets Alex can purchase with her $96.00 gift card, we can create an equation based on the costs of each item.

The cost of sketchbooks is $12.00 each, and the cost of paint sets is $15.00 each. We can express the total cost as follows:

\[ 12x + 15y = 96 \]

where \( x \) is the number of sketchbooks and \( y \) is the number of paint sets. Now, we can evaluate each option to see which combination meets the equation.

Option A: 1 sketchbook and 4 paint sets \[ x = 1, y = 4 \] \[ 12(1) + 15(4) = 12 + 60 = 72 \quad (\text{not valid}) \]

Option B: 3 sketchbooks and 4 paint sets \[ x = 3, y = 4 \] \[ 12(3) + 15(4) = 36 + 60 = 96 \quad (\text{valid}) \]

Option C: 4 sketchbooks and 3 paint sets \[ x = 4, y = 3 \] \[ 12(4) + 15(3) = 48 + 45 = 93 \quad (\text{not valid}) \]

Option D: 2 sketchbooks and 5 paint sets \[ x = 2, y = 5 \] \[ 12(2) + 15(5) = 24 + 75 = 99 \quad (\text{not valid}) \]

The only valid option is: B. 3 sketchbooks and 4 paint sets.