Mary has a goal of taking 8,000 more steps today. According to her pedometer, she has gotten 2,500 steps so far today. There are 5 hours left in the day. How many steps will she need to take each hour (assuming she walks the same number of steps each hour) for the rest of the day to meet her goal?

Write an inequality to model this situation, then solve.

A. [tex]5x + 2500 \ \textgreater \ 8000; \, x \ \textgreater \ 1,100[/tex]

B. [tex]2500x - 5x \ \textless \ 8000; \, x \ \textless \ 3,200[/tex]

C. [tex]5x + 8000 \ \textless \ 2500; \, x \ \textless \ 2,100[/tex]

D. [tex]5x + 2500 \ \textgreater \ 8000; \, x \ \textgreater \ 2,100[/tex]

Sure! Let's go through the problem step-by-step:

1. Understand the Goal: Mary wants to achieve a total of 8,000 steps today.

2. Current Steps: She has already walked 2,500 steps.

3. Steps She Still Needs: To find out how many more steps she needs to take, subtract the steps she has already taken from her goal:
[tex]\[
\text{Steps needed} = 8,000 - 2,500 = 5,500
\][/tex]

4. Time Left: There are 5 hours left in the day.

5. Steps Per Hour: We need to find out how many steps Mary should take per hour to meet her goal. We can determine this by dividing the remaining steps by the number of hours left:
[tex]\[
\text{Steps per hour} = \frac{5,500}{5} = 1,100
\][/tex]

6. Inequality: The problem asks to write an inequality to model the situation. The inequality is based on the steps per hour needing to be greater than the number we calculated:
[tex]\[
5x + 2,500 > 8,000
\][/tex]
Solve the inequality:
- Subtract 2,500 from both sides:
[tex]\[
5x > 5,500
\][/tex]
- Divide by 5:
[tex]\[
x > 1,100
\][/tex]

Therefore, Mary needs to walk more than 1,100 steps each hour for the rest of the day to meet her goal.