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

2 sketchbooks and 5 paint sets
2 sketchbooks and 5 paint sets

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

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

3 sketchbooks and 4 paint sets

Answer 1

To solve this problem, we need to set up the equation based on the costs of the sketchbooks and paint sets and ensure their total equals $96.

Let \( x \) be the number of sketchbooks and \( y \) be the number of paint sets. The cost is given by:

\[ 12x + 15y = 96 \]

Now let's evaluate each option:

1. 2 sketchbooks and 5 paint sets: \[ 12(2) + 15(5) = 24 + 75 = 99 \quad (\text{too much}) \]

2. 4 sketchbooks and 3 paint sets: \[ 12(4) + 15(3) = 48 + 45 = 93 \quad (\text{too little}) \]

3. 1 sketchbook and 4 paint sets: \[ 12(1) + 15(4) = 12 + 60 = 72 \quad (\text{too little}) \]

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

From the calculations, the only combination Alex can purchase, which totals exactly $96, is 3 sketchbooks and 4 paint sets.