Chelsea starts with $200 in her bank account. Every week she withdraws $15 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $65?
Write an inequality to represent the situation. Use x to represent the number of weeks.
Good work!
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
=
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= 8	x=9 (boundary)	x= 10
200 - 15x ≥ 65	
Good work!
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 
 
9
You got it!
What does x≤ 9 mean in this problem?

Chelsea has been withdrawing money for exactly 9 weeks or less than 9 weeks.

Chelsea has been withdrawing money for less than 9 weeks.

Chelsea has less than $9 in her account.

### Step 1: Write the Inequality  
The problem states Chelsea starts with **$200** and withdraws **$15** every week, maintaining a balance of at least **$65**. Let $x$ represent the number of weeks she makes withdrawals.

The inequality is:  
\[
200 - 15x \geq 65
\]

---

### Step 2: Solve the Equation to Find the Boundary  
We need to solve the equation $200 - 15x = 65$ to determine the maximum number of weeks she can make withdrawals.

1. Subtract 65 from 200:
   \[
   200 - 65 = 135
   \]
2. Divide by 15:
   \[
   x = \frac{135}{15} = 9
   \]

So, the boundary value is $x = 9$. This means Chelsea can withdraw money **for exactly 9 weeks** before the balance drops below $65.

---

### Step 3: Fill in the Truth Table for Different Values of $x$

Now let’s plug in values below, at, and above the boundary to see if the inequality $200 - 15x \geq 65$ holds.

| **x** | **Expression**           | **Result** | **Inequality True/False** |
|-------|--------------------------|------------|---------------------------|
| 8     | $200 - 15(8) = 80$     | $80 \geq 65$ | True                    |
| 9     | $200 - 15(9) = 65$     | $65 \geq 65$ | True                    |
| 10    | $200 - 15(10) = 50$    | $50 \geq 65$ | False                   |

---

### Step 4: Write the Solution to the Inequality  
From the truth table, we see that:

- The inequality is **True** when $x = 8$ and $x = 9$.  
- The inequality becomes **False** when $x = 10$.  

Thus, the solution to the inequality is:
\[
x \leq 9
\]

---

### Step 5: Interpret the Meaning of $x \leq 9$  

**What does $x \leq 9$ mean in this problem?**  

- **Correct Answer:** *Chelsea has been withdrawing money for exactly 9 weeks or less than 9 weeks.*

---

Let me know if you have any further questions!  
Here are five related questions to deepen your understanding:  
1. What would the inequality look like if Chelsea started with $300 instead?  
2. How would the solution change if the minimum balance needed was $100?  
3. If Chelsea deposits $10 each week instead of withdrawing, what would the new inequality be?  
4. How many weeks would it take for Chelsea's account to be empty if she continues withdrawing $15 each week?  
5. What if the amount she withdraws each week increases to $20? How would that change the inequality?

**Tip:** When solving inequalities, always remember to carefully handle signs when dividing or multiplying by negative numbers!

Chelsea starts with $200 in her bank account. Every week she withdraws $15 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $65? Write an inequality to represent the situation. Use x to represent the number of weeks.

Learn how to solve a real-world problem involving linear inequalities where Chelsea withdraws money weekly from her bank account. This example uses algebra to determine how many weeks Chelsea can withdraw while maintaining a minimum balance. Suitable for students in Grades 6-8.

Math Problem Statement

x

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation