SOLUTION: Eva invested a certain amount of money at 14% interest and $2000.00 more than that amount at 15%. Her total yearly interest was $1460.00. How much did she invest at each rate?

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Question 41827: Eva invested a certain amount of money at 14% interest and $2000.00 more than that amount at 15%. Her total yearly interest was $1460.00. How much did she invest at each rate?
Found 2 solutions by Nate, psbhowmick:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
x(.14) + (x + 2000)(.15) = 1460
.14x + .15x + 300 = 1460
.29x = 1160
x = 4000
$4,000 was invested at 14% while $6,000 was invested at 15%

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is solved assuming simple interest per annum (S.I.P.A).

Let us suppose that Eva invested $x at 14% S.I.P.A.
Therefore she invested $(x+2000) at 15% S.I.P.A.

Interest on $x for 1 year at 14% S.I.P.A. = $x%2A14%2F100
Interest on $(x+2000) for 1 year at 15% S.I.P.A. = $%28x%2B2000%29%2A15%2F100
Therefore total interest in 1 year = $x%2A14%2F100+%2B+%28x%2B2000%29%2A15%2F100 = $%2829x%2B30000%29%2F100.
Given, her total yearly interest was $1460.00.

Then, %2829x%2B30000%29%2F100+=+1460
or 29x + 30000 = 146000
or 29x = 146000 - 30000 = 116000
or x = 116000%2F29 = 4000

Hence, Eva invested $4,000.00 at 14% and $6,000.00 at 15% simple interest per annum.