Question

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 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 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.

Answer 1

To find out how many push-ups Jada needs to do each day for the rest of the week, we can set up an inequality.

1. **Total Push-ups Goal**: Jada wants to do at least 100 push-ups in total this week.
2. **Push-ups Already Done**: She has done 30 push-ups on Sunday.

Let \( x \) be the number of push-ups she will do each day for the remaining days of the week. There are 6 days left in the week (Monday to Saturday).

The inequality can be set up as follows:

\[
30 + 6x \geq 100
\]

Now, we will solve the inequality:

1. Subtract 30 from both sides:

\[
6x \geq 100 - 30
\]
\[
6x \geq 70
\]

2. Divide both sides by 6:

\[
x \geq \frac{70}{6}
\]
\[
x \geq \frac{35}{3} \approx 11.67
\]

Since Jada is doing whole push-ups, we round up to the nearest whole number, giving us:

\[
x \geq 12
\]

Now, let's interpret the solution in the context of the problem. Jada needs to do at least **12** push-ups each day for the rest of the week to meet her goal of 100 push-ups.

**The correct answer choice is:**
- Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.