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)
Let the number of push-ups Jada needs to do each day for the rest of the week be x. Then she needs to do x push-ups per day for 6 days (excluding Sunday). Since she has already done 30 push-ups on Sunday, the total number of push-ups she needs to do is 30 + 6x.
According to the problem, Jada wants the total number of push-ups she does this week to be at least 100. Therefore, we can write the inequality:
30 + 6x ≥ 100
Subtracting 30 from both sides, we have:
6x ≥ 70
Dividing both sides by 6, we get:
x ≥ 11.67
Since we cannot do a fraction of a push-up, we round up to the nearest whole number, which is 12.
Therefore, the solution to the inequality is x ≥ 12. This means that Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal of 100 push-ups.
The best interpretation of this solution in the context of the problem is that Jada needs to do at least 12 push-ups each day for the rest of the week in order to meet her goal of doing at least 100 push-ups over the course of the week.