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) costs $12.00, while each paint set (y) costs $15.00.

Question

Which of the following combinations of sketchbooks and paint sets can Alex purchase, assuming she spends her entire gift card?
(1 point)
• 3 sketchbooks and 4 paint sets
• 4 sketchbooks and 3 paint sets
• 2 sketchbooks and 5 paint sets
• 1 sketchbook and 4 paint sets

Answer 1

To determine which combinations of sketchbooks \(x\) and paint sets \(y\) Alex can purchase with her $96.00 gift card, we can represent the cost of her purchases with the following equation:

\[ 12x + 15y = 96 \]

where \(x\) is the number of sketchbooks and \(y\) is the number of paint sets.

Now, let’s evaluate each option:

1. 3 sketchbooks and 4 paint sets: \[ 12(3) + 15(4) = 36 + 60 = 96 \] This combination costs $96 and is valid.

2. 4 sketchbooks and 3 paint sets: \[ 12(4) + 15(3) = 48 + 45 = 93 \] This combination costs $93 and is not valid.

3. 2 sketchbooks and 5 paint sets: \[ 12(2) + 15(5) = 24 + 75 = 99 \] This combination costs $99 and is not valid.

4. 1 sketchbook and 4 paint sets: \[ 12(1) + 15(4) = 12 + 60 = 72 \] This combination costs $72 and is not valid.

After evaluating all combinations, the only valid combination that Alex can purchase with her entire gift card of $96.00 is:

• 3 sketchbooks and 4 paint sets.