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?

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) (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) (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.
Simplify and solve for P.
I've changed the decimals to fractions to simplify calculations.

Add the fractions on the left side.
Multiply both sides by 300.
Now divide both sides by 11.

The man's invested capital is $1,200,000

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