SOLUTION: This is the Question I had problems with: Catherine has $3000 to invest. She invests a sum of money at 9% per annum and the rest at 5% per annum. If the return on the higher inter

Question 766817: This is the Question I had problems with:
Catherine has $3000 to invest. She invests a sum of money at 9% per annum and the rest at 5% per annum. If the return on the higher interest rate is $95 more than the lower rate, how much did she invest at each rate?
Can you please help me? I only got as far as simplifying the information down to this: lower rate - x@5%
higher rate - x@9% + ($95+x@5%)

Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
Let her invest amount x at 5%
Then the amount invested at 9% = (3000 - x)
Return at 5% = x*5/100
Return at 9% = (3000 - x)*9/100 = 270 - 9*x/100
Difference between the 2 interests is given as 95. So we have the equation
270 - 9*x/100 = x*5/100 + 95
Simplifying
14*x/100 = 270 - 95 = 175
x = 175*100/14 = 1250
So amount invested at 5% = $1250
Amount invested at 9% = 3000 - 1250 = $1750
Check for correctness:
Interest at 5% = 1250*5/100 = $62.5
Interest at 9% = 1750 * 9/100 = $157.5
Difference = 157.5 - 62.5 = $95 - correct.
:)

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