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)

Question

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

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

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

D. 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 follow these steps:

1. Initial Push-ups: Jada did 30 push-ups on Sunday.
2. Weekly Goal: Jada wants to do at least 100 push-ups this week.
3. Remaining Days: There are 6 days left in the week (Monday to Saturday).

Let \( x \) be the number of push-ups Jada needs to do each day for the remaining 6 days.

The inequality for the total number of push-ups Jada wants to achieve would be: \[ 30 + 6x \geq 100 \]

Now, we can solve for \( x \):

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

2. Divide both sides by 6: \[ x \geq \frac{70}{6} \] \[ x \geq \frac{35}{3} \approx 11.67 \]

Since Jada needs to do a whole number of push-ups each day, we round up to the next whole number: \[ x \geq 12 \]

This means Jada needs to do at least 12 push-ups each day for the remaining 6 days.

Conclusion:

The correct interpretation of the solution in the context of the problem is:

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