Problem 7

Choose the inequality that matches this situation.

Sarah will spend at most $26 on candy. Each item costs $3, and she has a coupon for a $5 discount.

1 answer

To represent the situation mathematically, we can let \( x \) be the number of candy items Sarah buys. Given that each item costs $3, the total cost for the candy items is \( 3x \). Since she has a coupon for a $5 discount, her effective spending will be \( 3x - 5 \).

Sarah wants to spend at most $26, which means:

\[ 3x - 5 \leq 26. \]

This is the inequality that matches the situation.

If we want to simplify the inequality to ensure it's in a standard form, we can add 5 to both sides:

\[ 3x \leq 31. \]

And then divide by 3:

\[ x \leq \frac{31}{3} \approx 10.33. \]

However, since \( x \) must be a whole number (because she can only buy whole pieces of candy), the most she can buy is 10 items.

Thus, the original inequality \( 3x - 5 \leq 26 \) captures the situation correctly.