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

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 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 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 14 push-ups each day for the rest of the week to meet her goal.

GPT-4o mini · Answer

To determine how many push-ups Jada needs to complete each day for the rest of the week, we start by establishing the total number of push-ups she needs to do and the amount she has already completed.

Jada's goal for the week: 100 push-ups
Push-ups completed on Sunday: 30 push-ups
Remaining push-ups to reach her goal: \[ 100 - 30 = 70 \text{ push-ups} \]
Days remaining in the week: 6 days (Monday through Saturday)

Let \( x \) be the number of push-ups Jada does each day for the remaining 6 days. Then, we can set up the following equation to represent the total push-ups she needs to complete for the week:

\[ 6x \geq 70 \]

To solve for \( x \), we divide both sides of the inequality by 6:

\[ x \geq \frac{70}{6} \] \[ x \geq 11.67 \]

Since Jada can only do whole push-ups, we round 11.67 up to the next whole number.

Thus, Jada needs to do at least 12 push-ups each day for the rest of the week.

Finally, interpreting this in the context of the problem, 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.