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 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.

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.

1 answer

To determine how many push-ups Jada needs to do each day for the rest of the week to meet her goal of 100 push-ups, let's define the variables and set up the inequality.

Jada has already completed 30 push-ups on Sunday. Therefore, she needs to complete:

\[ 100 - 30 = 70 \text{ push-ups} \]

for the rest of the week. Since there are 6 days left (Monday through Saturday), let \( x \) represent the number of push-ups she does each day for these 6 days. We can set up the following inequality:

\[ 6x \geq 70 \]

Now, we solve this inequality for \( x \):

  1. Divide both sides by 6:

\[ x \geq \frac{70}{6} \]

  1. Simplify \( \frac{70}{6} \):

\[ x \geq \frac{35}{3} \approx 11.67 \]

Since Jada cannot do a fraction of a push-up, she'll need to round up to the nearest whole number. Thus,

\[ x \geq 12 \]

This indicates that Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.

Among the answer choices provided, the correct interpretation of the solution in the context of the problem is:

Jada needs to do at least 12 push-ups each day for the rest of the week to meet her goal.