Question

Jada has 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 of push-ups each day for the rest of the week. Write and solve 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?(1 point)
Responses

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 at least 10 push-ups each day for the rest of the week to meet her goal.

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 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 day for the rest of the week to meet her goal.
Jada needs to do at least 14 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 solve this problem, let's first summarize what we know:

- Jada wants to do at least 100 push-ups in total for the week.
- She does 30 push-ups on Sunday.
- She plans to do the same number of push-ups each day for the remaining 6 days of the week (Monday to Saturday).

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

The total number of push-ups she will do for the week can be expressed as:

\[
30 + 6x
\]

To meet her goal of at least 100 push-ups, we can set up the following inequality:

\[
30 + 6x \geq 100
\]

Now, we will solve the inequality for \( x \):

1. Subtract 30 from both sides:

\[
6x \geq 70
\]

2. Divide both sides by 6:

\[
x \geq \frac{70}{6}
\]

Simplifying \( \frac{70}{6} \) gives:

\[
x \geq \frac{35}{3} \approx 11.67
\]

Since Jada can't do a fraction of a push-up, we will round up to the nearest whole number. Therefore:

\[
x \geq 12
\]

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

Now, let's look at the interpretation choices. The correct interpretation is:

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