Question

ruth has $40. here are the prices of some things she wants to buy:
1 concert ticket: $40
1 book: $5
click to select how many concert tickets and books ruth can buy. you can choose any combination that uses up all of her money.

Explanation:

Step1: Define variables

Let \( x \) be the number of concert tickets and \( y \) be the number of books. The cost equation is \( 40x + 5y = 40 \).

Step2: Simplify the equation

Divide the entire equation by 5: \( 8x + y = 8 \).

Step3: Find non - negative integer solutions

• When \( x = 0 \): \( y=8 - 8\times0=8 \).
• When \( x = 1 \): \( y=8 - 8\times1 = 0 \).

Answer:

One possible combination is 0 concert tickets and 8 books, or 1 concert ticket and 0 books. (If we consider using all money, another way: Let's check the case when \( x = 0 \), then total money for books is \( \$40 \), number of books \(=\frac{40}{5}=8\); when \( x = 1 \), total money for ticket is \( \$40 \), so books \( = 0 \).)