Jada had challenged herself to do at least 100 full push-ups this week. On Sunday she does 30 push ups. Her arms are sore, so she decides to do fewer push ups on the remaining days of the week. She wants to do the same number for push ups each day for the rest of the week. Write and olive an inequality for the number of push ups Jada needs to do each day for the rest of the week to meet her goal of 100 push ups. Which answer choice best interprets the solution in the context of the problem?

Question

Jada needs to do at least 12 push ups each day for the rest of the week to meet her goal.

Jada needs to do at least 14 push ups each for the rest of the week to meet her goal

Jada needs to do at least 10 push ups each day for the rest of the week to meet her goal

Jada needs to do push ups for at least 12 more days to meet her goal

Answer 1

To find the number of push-ups Jada needs to do each day for the rest of the week, we first establish the known facts:

1. Jada's goal is to complete at least 100 push-ups in total for the week.
2. She has already completed 30 push-ups on Sunday.
3. There are 6 remaining days in the week (Monday to Saturday).

Let \( x \) represent the number of push-ups Jada does each day from Monday to Saturday.

The inequality for her total push-ups for the week can be set up as follows:

\[ 30 + 6x \geq 100 \]

Now, we solve this inequality:

1. Subtract 30 from both sides: \[ 6x \geq 70 \]

2. Divide both sides by 6: \[ x \geq \frac{70}{6} \approx 11.67 \]

Since \( x \) must be a whole number (as you can't do a fraction of a push-up), we round up to the nearest whole number:

\[ x \geq 12 \]

This means Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal of at least 100 push-ups.

Interpreting this in the context of the problem, the best answer choice is:

"Jada needs to do at least 12 push ups each day for the rest of the week to meet her goal."