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Let's break down the problem to solve it step by step:

### Problem:
The investor had two stocks last year:
- Company A: worth \$5,640
- Company B: worth \$6,450

This year:
- The stock in Company A has decreased by 15%.
- The stock in Company B has decreased by 16%.

We need to find the **total percentage decrease** in the value of the investor's stock account overall.

### Step 1: Calculate the decrease in value for each stock.
For Company A:
- 15% decrease on \$5,640:
  \[
  \text{Decrease} = 0.15 \times 5,640 = 846
  \]
  New value of Company A stock:
  \[
  5,640 - 846 = 4,794
  \]

For Company B:
- 16% decrease on \$6,450:
  \[
  \text{Decrease} = 0.16 \times 6,450 = 1,032
  \]
  New value of Company B stock:
  \[
  6,450 - 1,032 = 5,418
  \]

### Step 2: Calculate the total value before and after.
- Total value last year = \$5,640 + \$6,450 = \$12,090
- Total value this year = \$4,794 + \$5,418 = \$10,212

### Step 3: Calculate the total decrease in value.
- Total decrease = \$12,090 - \$10,212 = \$1,878

### Step 4: Find the total percentage decrease.
\[
\text{Percentage decrease} = \left( \frac{1,878}{12,090} \right) \times 100 = 15.5\%
\]

### Final Answer:
The total percentage decrease in the investor's stock account is **15.5%**.

Let me know if you'd like more details or further explanations!

### Related questions:
1. How would the result change if Company A had only decreased by 10%?
2. What if both companies had decreased by 20% instead?
3. How do you calculate percentage increases in stock value?
4. How would you calculate the total percentage increase if both stocks had risen in value?
5. What is the difference between calculating the percentage change for individual stocks versus an entire portfolio?

### Tip:
When calculating percentage changes for multiple items, always account for the relative weights (values) of each item to find an accurate total percentage change.

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5640 and his stock in Company B was worth $6450. The stock in Company A has decreased 15% since last year and the stock in Company B has decreased 16%. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).

Learn how to calculate the total percentage decrease in an investor's stock account for Company A and Company B. The investor's stocks in Company A decreased by 15% and in Company B by 16%. Follow the detailed step-by-step solution to find the overall percentage decrease. Suitable for high school students in Grades 9-11.

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