SOLUTION: Lisa invested her lottery winnings of $48 000 in two different mutual funds*. At the end of one year one fund had earned 10.5% interest and the other fund had earned 12% interest.

Question 1182251: Lisa invested her lottery winnings of $48 000 in two different mutual funds*. At the end of one
year one fund had earned 10.5% interest and the other fund had earned 12% interest. If she
received a total of $5520 in interest, how much did she invest in each mutual fund?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x in one and earned .105x
48000-x in the other and earned .12 for 5760-.12x
the total is -0.015x+5760=5520
so -0.0105x=-240
divide both sides by -0.015
=$16000 at 10.5 interest or $1680
=$32000 at 12% interest or $3840
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Here is an alternative to the standard algebraic solution method shown by the other tutor. If the numbers are "nice", this method is faster and easier (for me, at least) than the formal algebra.

(1) Do the calculation to show that $5520 interest on an investment of $48,000 is an average interest rate of 11.5%.
(2) Observe the three interest rates 10.5, 11.5, and 12 on a number line and determine that the average of 11.5% is 2/3 of the way from 10.5% to 12%.
(3) That means 2/3 of the total was invested at the higher rate.

ANSWER: 2/3 of $48,000, or $32,000, at 12%; the other $16,000 at 10.5%.

CHECK: .12(32000)+.105(16000) = 3840+1680 = 5520

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