Last year, Charlie had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $2640 in interest. How much did he invest in each account? First account: Second account: $
Last year, Charlie had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $2640 in interest. How much did he invest in each account? First account: Second account: $
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![**Title: Solving a Tax Rate or Interest Rate Problem Using a System of Equations**
**Problem Statement:**
Last year, Charlie had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $2,640 in interest. How much did he invest in each account?
**Solution:**
- Let \( x \) be the amount invested in the first account (10% interest).
- Let \( y \) be the amount invested in the second account (8% interest).
**Equation System:**
1. \( x + y = 30,000 \) (The total amount invested)
2. \( 0.10x + 0.08y = 2,640 \) (The total interest earned)
**Instructions:**
- Calculate the values of \( x \) and \( y \) that satisfy both equations.
- Enter the values in the boxes provided:
- First account: $[\ \ ]
- Second account: $[\ \ ]
**Explanation and Check:**
- Press the "Explanation" button for detailed steps on solving the equations.
- Press the "Check" button to verify your answers.
*Note: Utilize algebraic methods to solve the equations, such as substitution or elimination.*
© 2020 McGraw-Hill Education. All Rights Reserved.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F299ab521-a5b0-47a9-a17f-05b75826b9b4%2Ff1376ac7-5e3c-4a16-be4a-76a8d027f6bd%2Fd8z8w1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving a Tax Rate or Interest Rate Problem Using a System of Equations**
**Problem Statement:**
Last year, Charlie had $30,000 to invest. He invested some of it in an account that paid 10% simple interest per year, and he invested the rest in an account that paid 8% simple interest per year. After one year, he received a total of $2,640 in interest. How much did he invest in each account?
**Solution:**
- Let \( x \) be the amount invested in the first account (10% interest).
- Let \( y \) be the amount invested in the second account (8% interest).
**Equation System:**
1. \( x + y = 30,000 \) (The total amount invested)
2. \( 0.10x + 0.08y = 2,640 \) (The total interest earned)
**Instructions:**
- Calculate the values of \( x \) and \( y \) that satisfy both equations.
- Enter the values in the boxes provided:
- First account: $[\ \ ]
- Second account: $[\ \ ]
**Explanation and Check:**
- Press the "Explanation" button for detailed steps on solving the equations.
- Press the "Check" button to verify your answers.
*Note: Utilize algebraic methods to solve the equations, such as substitution or elimination.*
© 2020 McGraw-Hill Education. All Rights Reserved.
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