on two investments totaling $12,500, jessica lost 7% on one and earned 8% on the other. if her net annual…

on two investments totaling $12,500, jessica lost 7% on one and earned 8% on the other. if her net annual receipts were $271, how much was each investment? answerhow to enter your answer (opens in new window) 2 points $ at -7% $ at 8%

on two investments totaling $12,500, jessica lost 7% on one and earned 8% on the other. if her net annual receipts were $271, how much was each investment? answerhow to enter your answer (opens in new window) 2 points $ at -7% $ at 8%

Answer

Explanation:

Step1: Let the amount invested at -7% be $x$.

Then the amount invested at 8% is $(12500 - x)$.

Step2: Calculate the net - gain equation.

The loss on the first investment is $0.07x$ and the gain on the second investment is $0.08(12500 - x)$. The net annual receipts are given by the gain minus the loss, so $0.08(12500 - x)-0.07x = 271$.

Step3: Expand the equation.

$0.08\times12500-0.08x - 0.07x=271$. $1000-0.08x - 0.07x = 271$.

Step4: Combine like - terms.

$1000-(0.08x + 0.07x)=271$. $1000 - 0.15x=271$.

Step5: Isolate the variable $x$.

Subtract 1000 from both sides: $-0.15x=271 - 1000=-729$. Then divide both sides by - 0.15: $x=\frac{-729}{-0.15}=4860$.

Step6: Find the other investment amount.

The amount invested at 8% is $12500 - 4860 = 7640$.

Answer:

$4860$ at - 7% $7640$ at 8%