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 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.
Let's denote the number of push-ups Jada needs to do each day for the rest of the week as "x".
Since she already did 30 push-ups on Sunday, the total number of push-ups she needs to do for the week is 100 - 30 = 70.
To meet her goal, Jada needs to do at least 70 push-ups in the remaining days of the week.
Since there are 7 days in a week and she wants to do the same number of push-ups each day, we can write the inequality:
x * 6 ≥ 70
Simplifying this inequality, we get:
6x ≥ 70
Dividing both sides by 6, we get:
x ≥ 11.666...
Since Jada cannot do a fractional number of push-ups, the minimum number of push-ups she needs to do each day for the rest of the week is 12.
Therefore, the correct interpretation is:
Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.