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 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.

GPT-4o mini · Answer

Let's break down the problem step by step.

Calculate the push-ups Jada has already done: Jada has done 30 push-ups on Sunday.
Determine the total number of push-ups needed: Jada wants to do a total of at least 100 push-ups this week.
Set up the inequality: Let \( x \) be the number of push-ups Jada does each day for the remaining 6 days (Monday to Saturday). After Sunday, the total number of push-ups she will do is: \[ 30 + 6x \] To meet her goal of 100 push-ups, we can set up the inequality: \[ 30 + 6x \geq 100 \]
Solve the inequality: Subtract 30 from both sides: \[ 6x \geq 70 \] Now divide both sides by 6: \[ x \geq \frac{70}{6} \approx 11.67 \]

Since Jada can only do a whole number of push-ups, we round up to the next whole number: \[ x \geq 12 \]
Interpret the solution: This means Jada needs to do at least 12 push-ups each day for the rest of the week (Monday through Saturday) to meet her goal of 100 push-ups.

Conclusion:

The best answer choice that interprets 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.