SOLUTION: An executive invests $21,000, some at 6% and the rest at 5% annual interest. If he receives an annual return of $1,180, how much is invested at each rate?

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Question 1163997: An executive invests $21,000, some at 6% and the rest at 5% annual interest. If he receives an annual return of $1,180, how much is invested at each rate?
Found 3 solutions by Edwin McCravy, MathTherapy, greenestamps:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
This is a mixture problem.  
They are mostly all of this form:



This is a case where the second amount is given.                                                                                                                                                       



We change the percents to decimals



We multiply the 2nd equation through by 100 to clear
the decimals



Solve by either substitution or elimination.

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
An executive invests $21,000, some at 6% and the rest at 5% annual interest. If he receives an annual return of $1,180, how much is invested at each rate?
Let amount invested at 6% be S

Then amount invested at 5% is: 21,000 - S

We then get: .06S + .05(21,000 - S) = 1,180

.06S + 1,050 - .05S = 1,180

.01S = 130

Amount invested at 6%, or 

Based on provided info, do you think you can find the amount invested at 5%? 

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


If a formal algebraic solution is not required, here is a quick and easy informal way of solving two part "mixture" problems like this.


All $21,000 invested at 5% would yield $1050 interest; all at 6% would yield $1260 interest.


The actual interest was $1180.


Picture the three amounts on a number line: 1050, 1180, and 1260.  1180 is 13/21 of the way from 1050 to 1260.  (1050 to 1260 is a difference of 210; 1050 to 1180 is a difference of 120; 130/210 = 13/21.)


That means 13/21 of the total was invested at the higher rate.


ANSWER: 13/21 of $21,000, or $13,000, at 6%; the other $8000 at 5%.


CHECK:

.06(13000)+.05(8000) = 780+400 = 1180


 

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