Question
Leah starts with $250 in her bank account. Every week she withdraws $20 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $90?
Write an inequality to represent the situation. Use x to represent the number of weeks.
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 90, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 90
250−20x
=
90
x
=
Nice!
Fill in the table to show whether a value below the boundary, the boundary, and a value above the boundary make the inequality true or false.
x= 7 x=8 (boundary) x= 9
250 - 20x ≥ 90
You got it!
Now use your table to help you write the solution to the inequality.
x= 7 x=8 (boundary) x= 9
250 - 20x ≥ 90 True True False
x
Write an inequality to represent the situation. Use x to represent the number of weeks.
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 90, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 90
250−20x
=
90
x
=
Nice!
Fill in the table to show whether a value below the boundary, the boundary, and a value above the boundary make the inequality true or false.
x= 7 x=8 (boundary) x= 9
250 - 20x ≥ 90
You got it!
Now use your table to help you write the solution to the inequality.
x= 7 x=8 (boundary) x= 9
250 - 20x ≥ 90 True True False
x
Answers
GPT-4o mini
To determine how many weeks Leah can withdraw money while maintaining at least $90 in her bank account, we start with the inequality:
\[
250 - 20x \geq 90
\]
Here, \(x\) represents the number of weeks Leah can withdraw $20.
### Solve the inequality:
1. Start with the inequality:
\[
250 - 20x \geq 90
\]
2. Subtract 250 from both sides:
\[
-20x \geq 90 - 250
\]
\[
-20x \geq -160
\]
3. Divide both sides by -20. Remember to reverse the inequality when dividing by a negative number:
\[
x \leq \frac{-160}{-20}
\]
\[
x \leq 8
\]
This means Leah can withdraw for a maximum of 8 weeks while maintaining at least $90.
### Check with the boundary condition \(x = 8\):
Now let's solve the equation \(250 - 20x = 90\) to confirm the boundary:
1. Set the equation:
\[
250 - 20x = 90
\]
2. Subtract 250 from both sides:
\[
-20x = 90 - 250
\]
\[
-20x = -160
\]
3. Divide by -20:
\[
x = \frac{-160}{-20} = 8
\]
The boundary value is \(x = 8\).
### Construct the truth table:
Now to verify with the table for different values:
| \(x\) | \(250 - 20x \geq 90\) | True/False |
|---------|-----------------------|------------|
| \(7\) | \(250 - 20(7) = 250 - 140 = 110 \geq 90\) | True |
| \(8\) | \(250 - 20(8) = 250 - 160 = 90 \geq 90\) | True |
| \(9\) | \(250 - 20(9) = 250 - 180 = 70 \geq 90\) | False |
### Conclusion:
The results in the table show:
- For \(x = 7\): True
- For \(x = 8\): True (boundary)
- For \(x = 9\): False
Thus, the solution to the inequality is:
\[
x \leq 8
\]
This means Leah can withdraw money for **a maximum of 8 weeks** while keeping at least $90 in her account.
\[
250 - 20x \geq 90
\]
Here, \(x\) represents the number of weeks Leah can withdraw $20.
### Solve the inequality:
1. Start with the inequality:
\[
250 - 20x \geq 90
\]
2. Subtract 250 from both sides:
\[
-20x \geq 90 - 250
\]
\[
-20x \geq -160
\]
3. Divide both sides by -20. Remember to reverse the inequality when dividing by a negative number:
\[
x \leq \frac{-160}{-20}
\]
\[
x \leq 8
\]
This means Leah can withdraw for a maximum of 8 weeks while maintaining at least $90.
### Check with the boundary condition \(x = 8\):
Now let's solve the equation \(250 - 20x = 90\) to confirm the boundary:
1. Set the equation:
\[
250 - 20x = 90
\]
2. Subtract 250 from both sides:
\[
-20x = 90 - 250
\]
\[
-20x = -160
\]
3. Divide by -20:
\[
x = \frac{-160}{-20} = 8
\]
The boundary value is \(x = 8\).
### Construct the truth table:
Now to verify with the table for different values:
| \(x\) | \(250 - 20x \geq 90\) | True/False |
|---------|-----------------------|------------|
| \(7\) | \(250 - 20(7) = 250 - 140 = 110 \geq 90\) | True |
| \(8\) | \(250 - 20(8) = 250 - 160 = 90 \geq 90\) | True |
| \(9\) | \(250 - 20(9) = 250 - 180 = 70 \geq 90\) | False |
### Conclusion:
The results in the table show:
- For \(x = 7\): True
- For \(x = 8\): True (boundary)
- For \(x = 9\): False
Thus, the solution to the inequality is:
\[
x \leq 8
\]
This means Leah can withdraw money for **a maximum of 8 weeks** while keeping at least $90 in her account.