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)
Responses

1 sketchbook and 4 paint sets
1 sketchbook and 4 paint sets

3 sketchbooks and 4 paint sets
3 sketchbooks and 4 paint sets

​​​​ 4 sketchbooks and 3 paint sets
​​​​ 4 sketchbooks and 3 paint sets

2 sketchbooks and 5 paint sets

Answer 1

To find out which combination of sketchbooks and paint sets Alex can purchase with her $96 gift card, we can write the equation based on the costs:

Let \( x \) be the number of sketchbooks and \( y \) be the number of paint sets. The costs are:

• Each sketchbook costs $12: \( 12x \)
• Each paint set costs $15: \( 15y \)

The total cost equation is: \[ 12x + 15y = 96 \]

Now let's check each option:

1. 1 sketchbook and 4 paint sets: \[ 12(1) + 15(4) = 12 + 60 = 72 \quad \text{(Not equal to 96)} \]

2. 3 sketchbooks and 4 paint sets: \[ 12(3) + 15(4) = 36 + 60 = 96 \quad \text{(Equal to 96)} \]

3. 4 sketchbooks and 3 paint sets: \[ 12(4) + 15(3) = 48 + 45 = 93 \quad \text{(Not equal to 96)} \]

4. 2 sketchbooks and 5 paint sets: \[ 12(2) + 15(5) = 24 + 75 = 99 \quad \text{(Not equal to 96)} \]

From the evaluation, the only combination that allows Alex to spend her entire gift card is:

3 sketchbooks and 4 paint sets.