Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account? 

To determine how many weeks Keith can withdraw money from his savings account, we can set up the following inequality based on the given information:

- Keith starts with $500 in his account.
- He wants to have at least $200 left at the end of the summer.
- He withdraws $25 per week.

### Step 1: Define the variables
Let $ w $ represent the number of weeks he withdraws money.

### Step 2: Set up the inequality
Each week, Keith withdraws $25, so after $ w $ weeks, he will have withdrawn $ 25w $ dollars. The total amount left in his account after $ w $ weeks is:

\[
500 - 25w
\]

We want this amount to be at least $200, so we write the inequality:

\[
500 - 25w \geq 200
\]

### Step 3: Solve the inequality

1. Subtract 200 from both sides:

\[
500 - 25w \geq 200
\]
\[
500 - 25w - 200 \geq 0
\]
\[
300 - 25w \geq 0
\]

2. Subtract 300 from both sides:

\[
-25w \geq -300
\]

3. Divide by -25, remembering to flip the inequality sign:

\[
w \leq \frac{300}{25}
\]
\[
w \leq 12
\]

### Final Answer:
Keith can withdraw money for up to **12 weeks** before his balance drops below $200.

Would you like more details or have any further questions?

Here are 5 related questions for more practice:
1. If Keith wanted to have at least $300 at the end of the summer, how many weeks could he withdraw money?
2. What if Keith increased his weekly withdrawals to $30, how many weeks could he withdraw?
3. How much money will Keith have after 10 weeks of withdrawals?
4. If Keith's account had an interest rate, how would that affect the calculation?
5. What if Keith made an additional deposit of $100 halfway through the summer?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when dividing or multiplying by a negative number.

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account?

Find out how many weeks Keith can withdraw $25 per week from his $500 savings account while ensuring he has at least $200 left. Learn to solve this linear inequality step-by-step, using key algebraic concepts. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation