Kerry earned a total of $900 last year on his investments. If $7000 was invested at a certain rate of return and $9000 was invested in a fund with a rate that was 2% higher, find the two rates of interest.
Kerry earned a total of $900 last year on his investments. If $7000 was invested at a certain rate of return and $9000 was invested in a fund with a rate that was 2% higher, find the two rates of interest.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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This is a solving system of linear equations question I solved it already can you create a table solving the problem and using my calculations
![## Finding Rates of Interest on Investments
Kerry earned a total of $900 last year on his investments. If $7000 was invested at a certain rate of return and $9000 was invested in a fund with a rate that was 2% higher, we need to find the two rates of interest.
Given:
- Total earnings from investments: $900
- Amount invested at a certain rate: $7000
- Amount invested at a rate 2% higher: $9000
Let \( x \) be the rate of interest at which $7000 is invested and \( x+2 \) be the rate of interest at which $9000 is invested.
This implies:
\[ \frac{7000 \cdot x}{100} + \frac{9000 \cdot (x+2)}{100} = 900 \]
Simplifying the equation:
\[ 70x + 90x + 180 = 900 \]
\[ 160x = 900 - 180 \]
\[ 160x = 720 \]
\[ x = \frac{720}{160} \]
\[ x = \frac{9}{2} \]
\[ x = 4.5 \]
This means:
- $7000 was invested at a 4.5% rate of interest.
- $9000 was invested at \( x + 2 = 4.5 + 2 = 6.5 \%\) rate of interest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2c5c293-7ff8-490b-b548-13e2f43ca7a8%2F510b62c1-78d9-48e8-8a24-5e8bc3ded1a8%2Fu9gc486.jpeg&w=3840&q=75)
Transcribed Image Text:## Finding Rates of Interest on Investments
Kerry earned a total of $900 last year on his investments. If $7000 was invested at a certain rate of return and $9000 was invested in a fund with a rate that was 2% higher, we need to find the two rates of interest.
Given:
- Total earnings from investments: $900
- Amount invested at a certain rate: $7000
- Amount invested at a rate 2% higher: $9000
Let \( x \) be the rate of interest at which $7000 is invested and \( x+2 \) be the rate of interest at which $9000 is invested.
This implies:
\[ \frac{7000 \cdot x}{100} + \frac{9000 \cdot (x+2)}{100} = 900 \]
Simplifying the equation:
\[ 70x + 90x + 180 = 900 \]
\[ 160x = 900 - 180 \]
\[ 160x = 720 \]
\[ x = \frac{720}{160} \]
\[ x = \frac{9}{2} \]
\[ x = 4.5 \]
This means:
- $7000 was invested at a 4.5% rate of interest.
- $9000 was invested at \( x + 2 = 4.5 + 2 = 6.5 \%\) rate of interest.
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