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

 

True

False

False

 

True

False

Answer 1

Let's fill in the table based on the values of \( x \) provided:

- For \( x = 5 \):
\[
100 - 6(5) = 100 - 30 = 70
\]
Since \( 70 < 64 \) is false, we write **False** for \( x = 5 \).

- For \( x = 6 \) (the boundary):
\[
100 - 6(6) = 100 - 36 = 64
\]
Since \( 64 < 64 \) is false, we write **False** for \( x = 6 \).

- For \( x = 7 \):
\[
100 - 6(7) = 100 - 42 = 58
\]
Since \( 58 < 64 \) is true, we write **True** for \( x = 7 \).

Now, we can fill in the table:

\[
\begin{array}{|c|c|c|}
\hline
x & 100 - 6x < 64 \\
\hline
5 & \text{True} \\
6 & \text{False} \\
7 & \text{True} \\
\hline
\end{array}
\]

Overall, the filled table would look like this:

| \( x \) | \( 100 - 6x < 64 \) |
|---------|----------------------|
| 5 | True |
| 6 | False |
| 7 | True |

So, the correct responses based on calculations would be:

- \( x = 5 \): True
- \( x = 6 \): False
- \( x = 7 \): True

Let me know if you need further help!