SOLUTION: Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.The total income from all 3 investments is $1600. The income from the 5% and 6% i

Question 1162620: Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same as the income from the 8% investment. Find the amount invested at each rate
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%.
The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same
as the income from the 8% investment. Find the amount invested at each rate.
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In this problem, the key phrase is that saying The income from the 5% and 6% investments is the same as the income from the 8% investment. It means that the income from 8% investment is half of the total interest of $1600, i.e. $800. Next, since the interest of the 8% investment is $800, it means that the amount of the 8% investment is = 10000 dollars. Thus, we just know that the 8% investment was $10000; hence, the parts invested at 5% and 6%, make the rest $25000-$10000 = $15000. Doing in this way, we just reduced the problem from 3 unknowns to only 2, and the rest of the problem can be solved using one unknown, only. Let x be the amount invested at 6%; then the amount invested at 5% is (15000-x) dollars. The total interest equation for these two parts is 0.05*(15000-x) + 0.06x = 800 dollars (another half of $1600). From this equation, x = = 5000. Thus we have the ANSWER : $5000 was invested at 6%; 15000-5000 = 10000 dollars was invested at 5% and $10000 was invested at 8%. CHECK. 0.06*5000 + 0.05*10000 + 0.08*10000 = 1600 dollars, which is precisely correct total interest.

Solved.

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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

There was $800 of income from the 8% investment, and there was $800 of income combined from the 5% and 6% investments.

$800 income from an 8% investment means the amount invested at that rate was $10,000.

So the combined amounts invested in the 5% and 6% investments was $15,000.

$15,000 all invested at 5% would yield $750 income; all at 6% would yield $900 income.
The actual income from those two investments, $800, is one-third of the way from $750 to $900. That means 1/3 of the remaining $15,000 was invested at the higher rate. So $5000 at 6% and $10,000 at 5%.

ANSWER: $10,000 at 8%; $10,000 at 5%, and $5000 at 6%.

CHECK:
.08(10,000)+.05(10,000)+.06(5000) = 800+500+300 = 1600

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