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?
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 x represent the number of push-ups Jada needs to do each day for the rest of the week. The total number of push-ups Jada needs to do is 100 - 30 = 70. Since Jada wants to do the same number of push-ups each day for the rest of the week, she needs to do x push-ups for 7 - 1 = 6 days.
Therefore, the inequality is 6x ≥ 70.
To solve for x, we divide both sides of the inequality by 6:
x ≥ 70 ÷ 6 ≈ 11.67.
Since Jada cannot do a fraction of a push-up, she needs to do at least 12 push-ups each day for the rest of the week to meet her goal.
Therefore, the best answer choice is "Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal."