An investor invested a total of $2,500 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $122, how much was invested in each mutual fund?
An investor invested a total of $2,500 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $122, how much was invested in each mutual fund?
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.3: Solve Mixture Applications
Problem 206E: Laurie was completing the treasurer’s report for her son’s Boy Scout troop at the end of the school...
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![**Example Problem: Investing in Mutual Funds**
*An investor invested a total of $2,500 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $122, how much was invested in each mutual fund?*
---
**Solution:**
1. Let \( x \) be the amount invested in the mutual fund that earned a 6% profit.
2. Let \( y \) be the amount invested in the mutual fund that earned a 2% profit.
Since the total investment is $2,500, we have:
\[ x + y = 2500 \]
The total profit from the investments is $122. Given the profit percentages, we can write:
\[ 0.06x + 0.02y = 122 \]
---
**Equations:**
1. \( x + y = 2500 \)
2. \( 0.06x + 0.02y = 122 \)
Use these equations to solve for \( x \) and \( y \).
---
**Results:**
* The amount invested in the mutual fund that earned 6% was $ \( \_\_\_\_ \).
* The amount invested in the mutual fund that earned 2% was $ \( \_\_\_\_ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F375a8daa-a061-40df-aa13-f324a3b06fab%2F3f8ee44f-0695-44ca-a0d8-9bdc11972635%2Fldkfov_processed.png&w=3840&q=75)
Transcribed Image Text:**Example Problem: Investing in Mutual Funds**
*An investor invested a total of $2,500 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $122, how much was invested in each mutual fund?*
---
**Solution:**
1. Let \( x \) be the amount invested in the mutual fund that earned a 6% profit.
2. Let \( y \) be the amount invested in the mutual fund that earned a 2% profit.
Since the total investment is $2,500, we have:
\[ x + y = 2500 \]
The total profit from the investments is $122. Given the profit percentages, we can write:
\[ 0.06x + 0.02y = 122 \]
---
**Equations:**
1. \( x + y = 2500 \)
2. \( 0.06x + 0.02y = 122 \)
Use these equations to solve for \( x \) and \( y \).
---
**Results:**
* The amount invested in the mutual fund that earned 6% was $ \( \_\_\_\_ \).
* The amount invested in the mutual fund that earned 2% was $ \( \_\_\_\_ \).
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