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 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.

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 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.
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GPT-4o mini · Answer

To solve the problem, first, we need to establish how many push-ups Jada has left to do after Sunday.

Jada did 30 push-ups on Sunday.
Her goal is at least 100 push-ups for the week.
Therefore, the number of push-ups she has left to do is: \[ 100 - 30 = 70 \text{ push-ups} \]

Next, we need to determine how many days are left in the week after Sunday. 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.

We can now set up the inequality: \[ 6x \geq 70 \]

To solve for \( x \), divide both sides by 6: \[ x \geq \frac{70}{6} \] \[ x \geq 11.67 \]

Since Jada can only do whole push-ups, we round up to the nearest whole number: \[ x \geq 12 \]

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

The correct 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.