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?
A. Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.
B. Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal
C. Jada needs to do at least 14 push-ups each day for the rest of the week to meet her goal
D. Jada needs to do push-ups for at least 12 more days to meet her goal
Let's represent the number of push-ups Jada needs to do each day for the rest of the week as x. She has already done 30 push-ups on Sunday. Therefore, the total number of push-ups she will do in the week is 30 + 7x (30 from Sunday and 7x for the remaining 7 days of the week).
We want this total number of push-ups to be at least 100. So we can write the inequality as:
30 + 7x ≥ 100
To solve for x, we need to isolate it on one side of the inequality. Subtract 30 from both sides:
7x ≥ 70
Then, divide both sides by 7 to solve for x:
x ≥ 10
So Jada needs to do at least 10 push-ups each day for the rest of the week to meet her goal.
Answer choice A best interprets the solution in the context of the problem.