SOLUTION: This is a word problem my niece had in her homework assignment. She asked me to help her with it and she was trying to set it up completely different from the way I learned when I

Question 369399: This is a word problem my niece had in her homework assignment. She asked me to help her with it and she was trying to set it up completely different from the way I learned when I was in high school. The more I try to figure out how to set the problem up, the more confused I become and I can't remember how to do this. The problem is as follows:
Gary has $500 more invested at 12% than he has invested at 10%. The ratio of the amount invested at 12% to what is invested at 10% is 7 to 5. How much does he have invested at 10%?
I know that somewhere in the equation it should say .12 + 500, but I can't remember what I'm supposed to do with the ratio portion and how to fit it in. I think it's division, but not sure 7/5, but do I put it with the .10?
I feel stupid that I can't figure this out and help her, but I'm getting desperate. The later it gets, the more my mind wants to shut down, but I want to get it! Thank you for your help!
Sara
email: sebsis3@comcast.net
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the interest percentages are spurious information ___ probably thrown in to cause confusion

the key is the ratio of the amounts of the two investments
___ we don't know the amounts , but we do know the ratio
___ so we put in a constant (fudge factor) and build an equation

7c = 5c + 500 ___ the ratio is 7 to 5 , with the larger amount being 500 more

2c = 500 ___ c = 250

so the two amounts are 1750 and 1250 (250 multiplied by 7 and 5, respectively)
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