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Let's break down the problem step by step to determine how Margaret's savings compare to Harper's.

We are given:
- Harper's savings: $ 4x + 16 $
- Margaret's savings: $ 8x + 32 $

Now, to find how Margaret's savings compare to Harper's, we can try to express Margaret's savings in terms of Harper's.

1. Factor both expressions to simplify them:
   - Harper's savings: $ 4x + 16 = 4(x + 4) $
   - Margaret's savings: $ 8x + 32 = 8(x + 4) $

   We can see that Margaret's savings are exactly twice Harper's savings because:
   \[
   8(x + 4) = 2 \times 4(x + 4)
   \]
   Therefore, Margaret's savings are 2 times Harper's savings.

The correct answer is **A. Margaret's amount saved is 2 times as much as Harper's amount saved.**

Let me know if you would like further explanation or have any questions!

Here are 5 related questions to practice:
1. If Harper's savings were represented by $ 5x + 20 $, and Margaret's by $ 10x + 40 $, how would their savings compare?
2. If Harper's savings were $ 3x + 9 $, and Margaret's were $ 6x + 18 $, what would the comparison be?
3. How would you solve a comparison where Harper's savings are $ 2x + 5 $, and Margaret's savings are $ 4x + 10 $?
4. What happens to the comparison if we subtract a constant from both Harper's and Margaret's savings?
5. If Margaret saved an additional $50, how would this affect the comparison?

**Tip**: Whenever comparing two expressions, try to factor both and see if a simple multiple or ratio can be found.

Harper has an amount of money saved that can be represented by the expression 4x + 16. Her friend Margaret has savings represented by the expression 8x + 32. Which describes how Margaret's amount of money saved compares to Harper's amount saved?

Determine how Margaret's savings, represented by the expression 8x + 32, compare to Harper's savings, represented by the expression 4x + 16. Learn about algebraic expressions, factoring, and comparing linear expressions with this step-by-step solution. Suitable for students in Grades 6-8.

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