SOLUTION: A man invests 1/3 of his capital at 3% and the remainder at 4%. What is the capital if his total income is 44 000?

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Question 507834: A man invests 1/3 of his capital at 3% and the remainder at 4%. What is the capital if his total income is 44 000?
Found 2 solutions by nerdybill, Earlsdon:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A man invests 1/3 of his capital at 3% and the remainder at 4%. What is the capital if his total income is 44 000?
.
Let x = capital
then
.03(x/3) + .04(2x/3) = 44000
multiplying both sides by 3:
.03(x) + .04(2x) = 132000
.03x + .08x = 132000
.11x = 132000
x = $1,200,000

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let P = the invested amount of capital. After changing the interest rate percentages to their decimal equivalents, we can write the equation that relates the interest earned on each of the two invested amounts to the total interest earned.
%281%2F3%29P%280.03%29%2B%282%2F3%29P%280.04%29+=+44000 Simplify and solve for P.
I've changed the decimals to fractions to simplify calculations.
%281%2F3%29P%283%2F100%29%2B%282%2F3%29P%284%2F100%29+=+44000
P%2F100%2B8P%2F300+=+44000 Add the fractions on the left side.
%283P%2B8P%29%2F300+=+44000 Multiply both sides by 300.
11P+=+13200000 Now divide both sides by 11.
P+=+1200000
The man's invested capital is $1,200,000