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 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 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.
Let's assume that Jada needs to do x push-ups each day for the rest of the week to meet her goal. She has already done 30 push-ups on Sunday. The total number of push-ups Jada needs to do for the rest of the week is 100 - 30 = 70 push-ups.
Since she wants to do the same number of push-ups each day for the rest of the week, the inequality becomes:
x * (number of days) ≥ 70
To find the number of days, we divide 70 by x:
(number of days) ≥ 70 / x
The smallest whole number greater than or equal to 70 / x gives us the minimum number of days Jada needs to do push-ups. Since the problem states that she needs to do push-ups for the rest of the week, which usually means 7 days, the answer choice that best interprets the solution is:
Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.