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Question 1127007: An investor placed her money in a venture paying 7% interest. If she had had another $1500, she would have been able to invest her money at 10% and would have gained an additional $255 in annual interest income. How much did she invest?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the amount she invested at 7%.
let x + 1500 = the amount she could have invested at 10%.
let y = the interest earned.
you have 2 equations that need to be solved simultaneously.
they are:
.07 * x = y
.10 * (x + 1500) = y + 255
solve both equations for y to get:
.07 * x = y
.10 * (x + 1500) - 255 = y
simplify the second equation and leave the first equation as is to get:
.07 * x = y
.10 * x + .10 * 1500 - 255 = y
simplify the second equation further and leave the first equation as is to get:
.07 * x = y
.10 * x - 105 = y
subtract the first equation from the second to get:
.03 * x - 105 = 0
add 105 to both sides of this equation to get:
.03 * x = 105
solve for x to get:
x = 105 /.03 = 3500.
3500 is the amount invested at 7%.
3500 + 1500 = 5000 is the amount that could have been invested at 10%, if she had the extra 1500.
.07 * 3500 = 245
.10 * 5000 = 500
500 - 245 = 255
interest on amount invested at 10% minus interest on amount invested at 7% = 255, as expressed in the problem statement.
solution looks good.
solution is that the amount that she invested at 7% is 3500.
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