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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 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 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 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.

1 answer

To find out how many push-ups Jada needs to do each day for the rest of the week to meet her goal, we can set up the inequality based on the information provided.

  1. Total push-ups Jada wants to achieve: 100 push-ups
  2. Push-ups done on Sunday: 30 push-ups
  3. Push-ups remaining: \( 100 - 30 = 70 \) push-ups
  4. Days remaining in the week: 6 days (Monday through Saturday)

Let \( x \) be the number of push-ups Jada needs to do each day for the rest of the week. The inequality can be written as:

\[ 6x \geq 70 \]

Now, solve the inequality:

  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 can only do whole push-ups, we round this value up to the nearest whole number. Therefore:

\[ x \geq 12 \]

This means 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.

Answer:

The best 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.