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
=
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
=
Answers
GPT-4o mini
To solve the equation \( 100 - 6x = 64 \), follow these steps:
1. **Subtract 100 from both sides**:
\[
-6x = 64 - 100
\]
\[
-6x = -36
\]
2. **Divide both sides by -6**:
\[
x = \frac{-36}{-6}
\]
\[
x = 6
\]
Now that we've solved the equation \( 100 - 6x = 64 \) and found that \( x = 6 \), this represents the boundary point for the inequality \( 100 - 6x < 64 \).
### Conclusion
The value \( x < 6 \) means that less than 6 minutes could have passed for the pool to have less than 64 gallons of water left.
1. **Subtract 100 from both sides**:
\[
-6x = 64 - 100
\]
\[
-6x = -36
\]
2. **Divide both sides by -6**:
\[
x = \frac{-36}{-6}
\]
\[
x = 6
\]
Now that we've solved the equation \( 100 - 6x = 64 \) and found that \( x = 6 \), this represents the boundary point for the inequality \( 100 - 6x < 64 \).
### Conclusion
The value \( x < 6 \) means that less than 6 minutes could have passed for the pool to have less than 64 gallons of water left.