Dean set a goal to do more than 900 push-ups this month. So far, he has done 230 push-ups, and there are 20 more days remaining this month. Dean will do the same number of push-ups on each remaining day.

Question

Part A

Create an inequality that represents the number of push-up,
, Dean must do on each remaining day to reach his goal.

Enter your inequality in the box.

Question 2
Part B

What is the minimum number of push-ups Dean must do on each remaining day to reach his goal?

Enter a number in the box.

push-ups

Answer 1

To determine how many push-ups Dean needs to do each remaining day to reach his goal of more than 900 push-ups, we can establish the inequality as follows:

Part A: Create an Inequality

Let \( x \) be the number of push-ups Dean must do each remaining day.

He has already completed 230 push-ups, and he has 20 days left. Therefore, the total number of push-ups he will complete can be represented by:

\[ 230 + 20x > 900 \]

This is the inequality representing the number of push-ups Dean needs to do.

Part B: Solve for Minimum Push-ups per Day

Now, we need to solve the inequality for \( x \):

1. Subtract 230 from both sides:

   \[ 20x > 900 - 230 \]

   \[ 20x > 670 \]

2. Divide both sides by 20:

   \[ x > \frac{670}{20} \]

   \[ x > 33.5 \]

Since he needs to do a whole number of push-ups, Dean must do at least 34 push-ups each day to satisfy the inequality.

Therefore, the minimum number of push-ups Dean must do on each remaining day is:

Part B Answer: 34 push-ups