Question

A small kiddie pool starts with 100 gallons of water. The pool is being drained at a constant rate of 6 gallons per minute. How many minutes could have passed if the pool now has less than 64 gallons of water left?

Write an inequality to represent the situation. Use x to represent the number of minutes.

100−6x<64

Excellent!

You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 6x = 64, to find the boundary for the inequality. Show your work or solve on paper.

100 - 6x < 64

100−6x

=

64

 

x

=

6

You got it!

You found that x = 6 is the solution to the associated equation and the boundary of the inequality. Does the boundary, x = 6, make the inequality true or false?

x= 5x=6 (boundary)x= 7100 - 6x < 64?

False

True

False

?

Good work!

You found the boundary made the inequality false. Fill in the table to show whether a value below the boundary and a value above the boundary make the inequality true or false.

x= 5x=6 (boundary)x= 7100 - 6x < 64

False

True

False

False

True

True

False

Nice!

Complete the statement so that it represents the solution to the inequality. You can use the table to help you.

x= 5x=6 (boundary)x= 7100 - 6x < 64FalseFalseTrue



>





<

>

 

Excellent!

Draw a number line to represent the solution.

100 - 6x < 64

x > 6

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

You got it!

What does x> 6 mean in this problem?

More than 6 minutes have passed if there are less than 64 gallons water in the pool.

There are more than 6 gallons of water in the pool.

There are less than 6 gallons of water in the pool.

Answers

GPT-4o mini
You are correct! The statement \( x > 6 \) means that more than 6 minutes have passed if there are less than 64 gallons of water left in the pool. This indicates that, after 6 minutes, the pool will have less than 64 gallons of water, and the solution \( x > 6 \) refers to the amount of time that has elapsed beyond that point.

So, the correct interpretation is:

**More than 6 minutes have passed if there are less than 64 gallons of water in the pool.**