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 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.

GPT-4o mini · Answer

To solve this problem, let's start by identifying how many push-ups Jada has left to do after Sunday.

Jada's weekly goal is at least 100 push-ups.
On Sunday, she does 30 push-ups.
Therefore, the number of push-ups she has left to do is \(100 - 30 = 70\) push-ups.

Since there are 6 remaining days in the week (Monday through Saturday), if we let \(x\) represent the number of push-ups Jada does each day for those 6 days, we can set up the inequality:

\[ 6x \geq 70 \]

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

Divide both sides of the inequality by 6:

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

Since Jada cannot do a fraction of a push-up, we round this 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.

Interpreting the solution: The correct interpretation from the choices provided is:

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