<PRE><B>Question 160678</B>
first thing you have to do is find out what the rest is.
several ways to do it.
one way is as follows:
1/2 + 1/3 + x = 1
solve for x.
easiest way is to multiply both sides of the equation by 6 to remove the denominators.
equation becomes
3 + 2 + 6*x = 6
6*x = 6 - 3 - 2 = 1
x = 1/6
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to see if that&#39;s correct, add up 1/2 + 1/3 + 1/6 to see if it adds up to 1.
1/3 is the same as 2/6.
1/2 is the same as 3/6
so 2/6 + 3/6 + 1/6 = 6/6 = 1.
x = 1/6 is good.
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you know what the total income each year is.
it&#39;s $530.
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now you know that:
1/2 of the money is invested at 5%.
1/3 of the money is invested at 4%.
1/6 of the money is invested at 3.5%
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if 1/2 of the money is invested at 5%, then the amount of income from 1/2 of the money at the end of the year is 5% times (1/2 of the money).
this also means that 4% times (1/3 of the money) give you the amount of income from 1/3 of the money at the end of the year.
this also means that 3.5% times (1/6) of the money) gives you the amount of income from 1/6 of the money
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let y = total amount of money invested.
let $530 = total income from money invested.
equation becomes:
5%*y*1/2 + 4%*y*1/3 + 3.5%*y*1/6 = $530
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this is the same as (5%*y)/2 + (4%*y)/3 + (3.5%*y)/6 = $530.
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to get the interest rate you have to divide by 100%.  
5% / 100% = .05
4% / 100% = .04
3.5% / 100% = .035
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you substitute interest rate for % interest and the equation becomes
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(.05*y)/2 + (.04*y)/3 + (.035*y)/6 = $530.
multiplying both sides of the equation by 6 to remove the denominators, and the equation becomes
3*.05*y + 2*.04*y + .035*y = 6*$530
which becomes
.15*y + .08*y + .035*y = $3180
which becomes
.265*y = $3180
which becomes
y = $3180/.265 which equals $12000.
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to prove that the answer is correct, you substitute $12000 for y and solve the original equation after you converted from % to rate.
that equation is .05*y*(1/2) + .04*y*(1/3) + .035*y*(1/6) = $530.
which becomes
.05*12000*(1/2) + .04*12000*(1/3) + .035*12000*(1/6) = $530.
which becomes
$300 + $160 + $70 = $530
which becomes
$530 = $530
which proves the equation is good.
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your answer is total money invested is $12000.

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