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) About Me  (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.                                                                                                                                                       

system%28x%2By=21000%2C%226%25%22x%2B%225%25%22y=1180%29

We change the percents to decimals

system%28x%2By=21000%2C0.06x%2B0.05y=1180%29

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

system%28x%2By=21000%2C6x%2B5y=118000%29

Solve by either substitution or elimination.

Edwin

Answer by MathTherapy(10552) About Me  (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) About Me  (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