Question
Michael starts with $200 in his bank account. Every week he withdraws $15 for miscellaneous expenses. For how many weeks could he withdraw the money if he maintains a balance of at least $65?
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, 200 - 15x = 65, to find the boundary for the inequality. Show your work or solve on paper.
200 - 15x ≥ 65
200−15x
=
65
−
−
=
x
=
Excellent!
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= 8 x=9 (boundary) x= 10
200 - 15x ≥ 65
Nice!
Now use your table to help you write the solution to the inequality.
x= 8 x=9 (boundary) x= 10
200 - 15x ≥ 65 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, 200 - 15x = 65, to find the boundary for the inequality. Show your work or solve on paper.
200 - 15x ≥ 65
200−15x
=
65
−
−
=
x
=
Excellent!
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= 8 x=9 (boundary) x= 10
200 - 15x ≥ 65
Nice!
Now use your table to help you write the solution to the inequality.
x= 8 x=9 (boundary) x= 10
200 - 15x ≥ 65 True True False
x
Answers
GPT-4o mini
Let's go through the problem step-by-step.
1. **Setting up the Inequality**:
Michael has $200 in his bank account and withdraws $15 every week. We want to maintain a balance of at least $65. The inequality can be represented as:
\[
200 - 15x \geq 65
\]
Here, \( x \) represents the number of weeks.
2. **Solving the Equation**:
To find the boundary, we set the inequality to equality:
\[
200 - 15x = 65
\]
Now, we solve for \( x \):
\[
200 - 15x = 65
\]
Subtract 200 from both sides:
\[
-15x = 65 - 200
\]
\[
-15x = -135
\]
Now, divide by -15 (remember to reverse the inequality when dividing by a negative number):
\[
x = \frac{-135}{-15} = 9
\]
3. **Testing Values in the Inequality**:
Now we will create a table to test values below, at, and above the boundary \( x = 9 \).
| \( x \) | \( 200 - 15x \geq 65 \) | Result |
|---------|--------------------------|--------|
| 8 | \( 200 - 15(8) = 200 - 120 = 80 \) | True |
| 9 | \( 200 - 15(9) = 200 - 135 = 65 \) | True |
| 10 | \( 200 - 15(10) = 200 - 150 = 50 \) | False |
4. **Writing the Solution**:
From the table, we see that values \( x = 8 \) and \( x = 9 \) make the inequality true, while \( x = 10 \) does not. Therefore, the solution to the inequality \( 200 - 15x \geq 65 \) is:
\[
x \leq 9
\]
So Michael can continue to withdraw money for **9 weeks or fewer** in order to maintain at least $65 in his account.
1. **Setting up the Inequality**:
Michael has $200 in his bank account and withdraws $15 every week. We want to maintain a balance of at least $65. The inequality can be represented as:
\[
200 - 15x \geq 65
\]
Here, \( x \) represents the number of weeks.
2. **Solving the Equation**:
To find the boundary, we set the inequality to equality:
\[
200 - 15x = 65
\]
Now, we solve for \( x \):
\[
200 - 15x = 65
\]
Subtract 200 from both sides:
\[
-15x = 65 - 200
\]
\[
-15x = -135
\]
Now, divide by -15 (remember to reverse the inequality when dividing by a negative number):
\[
x = \frac{-135}{-15} = 9
\]
3. **Testing Values in the Inequality**:
Now we will create a table to test values below, at, and above the boundary \( x = 9 \).
| \( x \) | \( 200 - 15x \geq 65 \) | Result |
|---------|--------------------------|--------|
| 8 | \( 200 - 15(8) = 200 - 120 = 80 \) | True |
| 9 | \( 200 - 15(9) = 200 - 135 = 65 \) | True |
| 10 | \( 200 - 15(10) = 200 - 150 = 50 \) | False |
4. **Writing the Solution**:
From the table, we see that values \( x = 8 \) and \( x = 9 \) make the inequality true, while \( x = 10 \) does not. Therefore, the solution to the inequality \( 200 - 15x \geq 65 \) is:
\[
x \leq 9
\]
So Michael can continue to withdraw money for **9 weeks or fewer** in order to maintain at least $65 in his account.