amantha is planning to take a trip. The cost of the plane ticket is $575. She earns $15 an hour (h) and has already saved $135. Which of the following inequalities shows the number of hours (h) Samantha could work in order to buy her ticket? Select two that apply.

Question

A.
15h + 135 ≤ 575

B.
15h + 135 ≥ 575

C.
15h ≥ 440

D.
15h ≥ 710

Answer 1

To determine how many hours Samantha needs to work to afford her plane ticket, we can set up the inequality based on her earnings and savings.

1. The total amount needed for the ticket is $575.
2. She has already saved $135.
3. The amount she still needs is: \( 575 - 135 = 440 \).
4. If she earns $15 per hour, her total earnings from working \( h \) hours is \( 15h \).

The inequality that shows how many hours she needs to work can be set up as follows:

\[ 15h + 135 \geq 575 \]

This indicates that her total money (savings plus earnings) should be at least $575.

Now, we can also rearrange this to see another form:

\[ 15h \geq 440 \]

This shows that her earnings alone should be at least $440, which is what she needs after considering her savings.

So, the correct answer is:

• A. \( 15h + 135 \leq 575 \) is not correct (it should be \(\geq\)).
• B. \( 15h + 135 \geq 575 \) is correct.
• C. \( 15h \geq 440 \) is correct.
• D. \( 15h \geq 710 \) is not correct (it exceeds the requirement).

Thus, the correct choices are:

B and C.