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 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 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 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.
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Since Jada has already done 30 push-ups on Sunday, she needs to do at least 70 more push-ups to meet her goal of 100 push-ups for the week. Since she wants to do the same number of push-ups each day for the rest of the week, we can represent the number of push-ups she needs to do each day as x. Therefore, we can write the inequality as:
x * (number of remaining days) >= 70
Since there are 6 remaining days in the week (Monday to Saturday), the inequality becomes:
x * 6 >= 70
To solve for x, we divide both sides of the inequality by 6:
x >= 70/6
x >= 11.67
Since Jada can't 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 correct answer choice is: Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.