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 decided 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?
Options:
Jada needs to do push-ups for at least 12 more days to meet her goal
Jada needs to do at least 12 push-up’s 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
Let x be the number of push-ups Jada needs to do each day for the rest of the week.
The total number of push-ups Jada will do during the week is 30 + (x * 6) (since there are 6 remaining days in the week).
We want this total to be at least 100, so we can write the inequality:
30 + (x * 6) ≥ 100
Simplifying the inequality, we get:
x * 6 ≥ 70
Dividing both sides of the inequality by 6, we get:
x ≥ 70/6 ≈ 11.67
Since Jada wants to do the same number of push-ups each day, she needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Therefore, the correct answer is:
Jada needs to do at least 12 push-up’s each day for the rest of the week to meet her goal. Answer choice B