Question
Emma 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 $110?
Write an inequality to represent the situation. Use x to represent the number of weeks.
You got it!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 110, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 110
250−20x
=
110
x
=
Write an inequality to represent the situation. Use x to represent the number of weeks.
You got it!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 110, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 110
250−20x
=
110
x
=
Answers
GPT-4o mini
To solve the equation \( 250 - 20x = 110 \), we need to isolate \( x \). Here are the steps:
1. Start with the equation:
\[
250 - 20x = 110
\]
2. Subtract \( 250 \) from both sides:
\[
-20x = 110 - 250
\]
\[
-20x = -140
\]
3. Now, divide both sides by \( -20 \). Remember that dividing by a negative number will flip the inequality if we were solving an inequality:
\[
x = \frac{-140}{-20}
\]
\[
x = 7
\]
Thus, the boundary solution is \( x = 7 \).
Now, we can write the complete inequality based on the problem statement:
\[
250 - 20x \geq 110
\]
This means Emma can withdraw $20 for \( x \) weeks as long as \( x \) is less than or equal to 7. Therefore, \( x \) can be any whole number from 0 to 7, making the maximum number of weeks she can withdraw $20 while maintaining at least a $110 balance equal to 7 weeks.
1. Start with the equation:
\[
250 - 20x = 110
\]
2. Subtract \( 250 \) from both sides:
\[
-20x = 110 - 250
\]
\[
-20x = -140
\]
3. Now, divide both sides by \( -20 \). Remember that dividing by a negative number will flip the inequality if we were solving an inequality:
\[
x = \frac{-140}{-20}
\]
\[
x = 7
\]
Thus, the boundary solution is \( x = 7 \).
Now, we can write the complete inequality based on the problem statement:
\[
250 - 20x \geq 110
\]
This means Emma can withdraw $20 for \( x \) weeks as long as \( x \) is less than or equal to 7. Therefore, \( x \) can be any whole number from 0 to 7, making the maximum number of weeks she can withdraw $20 while maintaining at least a $110 balance equal to 7 weeks.