Corinna has $64. She wants to buy a $251 plane ticket. She will save up her earnings from working at the museum where she earns $17 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $251?

Question

A.
n ≥ 11
B.
n ≤ 10
C.
n ≤ 11
D.
n ≥ 10

Answer 1

To determine the inequality that shows the number of hours, \( n \), Corinna must work so that she has a total of at least $251, we can set up the following equation:

Corinna starts with $64, and for every hour she works, she earns $17. Therefore, her total amount after working \( n \) hours can be expressed as:

\[ 64 + 17n \]

We want to find out when this amount is at least $251:

\[ 64 + 17n \geq 251 \]

Now, we can solve this inequality step by step:

1. First, subtract 64 from both sides:

\[ 17n \geq 251 - 64 \] \[ 17n \geq 187 \]

2. Then, divide both sides by 17:

\[ n \geq \frac{187}{17} \] \[ n \geq 11 \]

So the inequality that shows the number of hours, \( n \), Corinna must work is:

\[ n \geq 11 \]

Thus, the correct answer is:

A. \( n \geq 11 \)