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

Answer 1

To find out how many push-ups Jada needs to do each day for the rest of the week, we can follow these steps:

1. First, we determine how many push-ups she has already completed. Jada does 30 push-ups on Sunday, so:
\[
\text{Push-ups completed} = 30
\]

2. Jada's goal is to complete at least 100 push-ups for the week. Therefore, the number of push-ups she still needs to do is:
\[
\text{Push-ups remaining} = 100 - 30 = 70
\]

3. The week has 7 days, and she has already completed push-ups on 1 day (Sunday). That leaves her with 6 days (Monday through Saturday) to do push-ups. Let \( x \) be the number of push-ups she does each day for the remaining 6 days.

4. The inequality to represent the total number of push-ups for the week is:
\[
6x \geq 70
\]

5. To solve for \( x \), we divide both sides of the inequality by 6:
\[
x \geq \frac{70}{6} \approx 11.67
\]

Since Jada can only do whole push-ups, we round up to the nearest whole number. Therefore, Jada needs to do at least 12 push-ups each day for the remaining 6 days to meet her goal.

Thus, the best interpretation of the solution in the context of the problem is:

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