Question

avery has $12. here are the prices of some things she wants to buy:
1 ride ticket $3
1 soda $2
click to select how many ride tickets and sodas avery can buy. you can choose any combination that uses up all of her money.
ride tickets

sodas

Explanation:

Step1: Define variables

Let \( x \) be the number of ride tickets and \( y \) be the number of sodas. The cost equation is \( 3x + 2y = 12 \).

Step2: Find integer solutions

We can solve for \( y \): \( 2y = 12 - 3x \) → \( y=\frac{12 - 3x}{2} \). We need \( x \) and \( y \) to be non - negative integers.

• If \( x = 0 \), then \( y=\frac{12-0}{2}=6 \).
• If \( x = 2 \), then \( y=\frac{12 - 6}{2}=3 \).
• If \( x = 4 \), then \( y=\frac{12-12}{2}=0 \).

Let's take one of the solutions, for example, when \( x = 2 \) (ride tickets) and \( y = 3 \) (sodas). Let's verify: \( 3\times2+2\times3=6 + 6=12 \), which uses up all her money.

Answer:

One possible combination is 2 ride tickets and 3 sodas (other valid combinations are 0 ride tickets and 6 sodas, or 4 ride tickets and 0 sodas).