Question

sarahs dad bought her a scooter that cost $89.95. he figures he can spend up to $30.05 on a helmet before he spends too much money in all. let x represent how much money sarahs dad wants to spend in all. which inequality describes the problem? x - 89.95 ≤ 30.05; x - 89.95 > 30.05. solve the inequality. then, complete the sentence to describe the solution. sarahs dad wants to spend at most $blank in all.

Explanation:

Part 1: Choosing the Correct Inequality

The total amount spent is \( x \), and the scooter costs \( \$89.95 \). The amount spent on the helmet is \( x - 89.95 \), and this amount should be at most \( \$30.05 \) (since he can spend up to \( \$30.05 \) on the helmet). "At most" means less than or equal to, so the inequality is \( x - 89.95 \leq 30.05 \). The other inequality \( x - 89.95 > 30.05 \) would mean he spends more than \( \$30.05 \) on the helmet, which is not allowed.

Step 1: Add 89.95 to both sides

To solve \( x - 89.95 \leq 30.05 \), we add 89.95 to both sides of the inequality.
\( x - 89.95 + 89.95 \leq 30.05 + 89.95 \)

Step 2: Simplify both sides

Simplifying the left side: \( x - 89.95 + 89.95 = x \)
Simplifying the right side: \( 30.05 + 89.95 = 120 \)
So we get \( x \leq 120 \)

Answer:

\( x - 89.95 \leq 30.05 \)

Part 2: Solving the Inequality