Question 1132304
a certain amount was loaned at m%. Let "certain amount" be x. Then we have that x amount was loaned at m, or xm
Then, twice as much was at n%, so this amount = 2xn
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xm + 2xn = d <-- this, as the problem says, is the interest earned in one year.
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OK, so we know that the total amount is x + 2x, where x pays m% and 2x pays n%.
x + 2x = 3x
x/3x = 1/3x this means that m interest came from 1/3 of the money
2x/3x = 2/3x this means that n interest came from 2/3 of the money
d/(1/3xm + 2/3(2x)n) = total amount you invested.

NOTE: Sometimes to make it easier to understand it's better to use some numbers. Let's do it quickly:
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Money invested: 
x = 4, thus 2x = 8 (and the total invested is 4 + 8 = 12, but save this. We are going to calculate it)
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Interest
m = 10% and n = 20%
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4(0.1) + 8(0.20) = 2 this is the total interest earned.
Now, we said 1/3 of the interest is from x and 2/3 of the interest comes from 2x

0.10*1/3 + 0.20*2/3 = 0.03333 + 0.13333 = 0.16667
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Total interest earned was 2 and 2/0.16667 = 12 which is the amount you invested in this example.
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Happy learning