SOLUTION: A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investment is $91. How much is invested at 8%?

Question 78918: A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investment is $91. How much is invested at 8%?
Answer by mathdoc314(58) (Show Source): You can put this solution on YOUR website!

OK i will try to answer this one since I like answering and since my dad once tried to teach me about compound interest. Compound interest is not involved in this problem and it is hard to get a credit card company to give you their formula I think.
The problem says, as I see it,
X is invested at 10%
2X is invested at 8%
The total interest is $91
What is invested at 8% ?
where X is "a certain sum that is invested".
What you will do is solve for X using the given information, and then as the final anwer give 2x since that is the quantity requested in the problem statement.
Generally investment rates are computed per year, so I am assuming the investment period they are talking about is 1 year, and I don't have to worry about compounding it where you'd compute (1.10)^N (N is the number of years) or (1.08)^N either. They are just talking about some situation where you put your money in and later you get back 10% or 8% more and then the deal is done.
So you have X * (1.10) + 2X * (1.08) = 91 as your equation to solve
It helps to know when they say "percent" they are talking about hundredths. There are ten fingers on a person's hands, ten pennies in a dime, and a hundred pennies in a dollar, and a hundred centimetres in a metre, so being human and living on planet Earth means you know "percent" means a hundredth. Ten percent is written as 0.10 or 10/100 and when you earn ten percent that is added to 1 which is 1.00 so you can see 1.00 + 0.10 = 1.10 which is the original amount plus ten per cent interest.
Now you have 3.26 X = 91
I am using my calculator to divide 91/3.26 but you could also use long division
X = 91/ 3.26 = 27.92 and I have rounded up from 27.913 because I want to have at least $91 when I am done, not less. Your teacher may want you to round to X=27.91 instead.
The answer to the problem is closer to 55.83
Check this:
55.83 plus 8 percent = 60.30 (55.83 * 1.08)
27.91 plus 10 percent = 30.70 (27.91 * 1.10)
Total is 91.00

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