SOLUTION: The annual returns on sid carrington's three investments amounted to $21,600:6% on a savings account,8% on mutual funds and 12% on bonds.The amount of Sid's investment in bonds was

Question 1196399: The annual returns on sid carrington's three investments amounted to $21,600:6% on a savings account,8% on mutual funds and 12% on bonds.The amount of Sid's investment in bonds was twice the amount of his investment in the savings and the interest earned from his investment in bonds was equal to the dividends he recieved from his investment in mutual funds.Find how much money he placed in each type of investment
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
a = amount invested in savings
b = amount invested in mutual funds
c = amount invested in bonds
you get a + b + c = 21600
the investment in bonds = 2 * the investment in savings.
this means that c = 2a
solve for a to get a = 1/2 * c
the interest earned from bonds = the dividends from mutual funds.
this means that .12*c = .08*b
solve for b to get b = .12*c/.08 = 3/2 * c
replace a and b in the equation of a + b + c = 21600 to get:
1/2 * c + 3/2 * b + c = 21600
combine like terms to get 3 * c = 21600
solve for c to get c = 7200
since a = 1/2 * c, then a = 3600
since b = 3/2 * c, then b = 10800
consequently, a + b + c = 3600 + 10800 + 7200 = 21600.
this confirms the investment amounts are good.
also, .12*c = .08*b becomes .12 * 7200 = .08 * 10800 which becomes 864 = 864.
this confirms the interest on the investments in b and c are also correct.
your solution is that he placed 3600 in savings and 10800 in mutual funds and 7200 in bonds for a total investment of 21600.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The annual returns on sid carrington's three investments amounted to $21,600:
6% on a savings account,8% on mutual funds and 12% on bonds.
The amount of Sid's investment in bonds was twice the amount of his investment
in the savings and the interest earned from his investment in bonds was equal
to the dividends he recieved from his investment in mutual funds.
Find how much money he placed in each type of investment
~~~~~~~~~~~~

First sentence of this post says:

The annual returns on sid carrington's three investments amounted to $21,600: 6% on a savings account,8% on mutual funds and 12% on bonds.

Tutor @Theo solved and interpreted it as if three investments amounted to $21,000.

But it can be read as if three RETURNS amounted to $21,000.

In my view, as the problem is worded and printed, it is AMBIGOUS.

I would interpret it in different way than @Theo.

If a Math problem is ambiguous and admits different interpretations, it is very bad sign: such problem is not trustworthy.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The problem clearly states that the RETURNS from the three investments amounted to $21,600.

And the problem as stated is NOT ambiguous; the given conditions describe the problem completely.

Let x be the amount invested in savings.

The amount invested in bonds was twice as much: 2x.

The amount of interest on the bonds, 2x, at a return rate of 12%, was the same as the amount of dividends from the mutual funds, at a rate of 8%. Since the amounts of the returns are the same and the interest rates are in the ratio 12:8 = 3:2, the amounts invested in those two are in the ratio 2:3. Since the amount invested in bonds was 2x, the amount invested in mutual funds was 3x.

So we have amount x invested at 6%, amount 2x invested at 12%, and amount 3x invested at 8%, yielding total returns of $21,600:

.06(x)+.12(2x)+.08(3x) = 21,600
.06x+.24x+.24x = 21,600
.54x = 21,600
x = 21,600/.54 = 40,000

ANSWERS: The amounts invested in each type of investment were
savings: x = $40,000
bonds: 2x = $80,000
mutual funds: 3x = $120,000

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