On two investments totaling $12500 Lydia lost 7% on one and earned 8% on the other. If her net annual receipts were $115 how much was each investment
oops. make that
.08x - .07(12500-x) = 115
.08x - .07(12500) = 115
Let's assume the amount of money invested at a 7% loss is represented by 'x', and the amount invested at an 8% gain is represented by 'y'.
Given that the total investment amount is $12500, we can set up the following equation:
x + y = 12500
We also know that Lydia lost 7% on the first investment, which means she received 93% of that amount (100% - 7%). Additionally, she earned 8% on the second investment, which means she received 108% of that amount (100% + 8%).
From that information, we can set up another equation:
0.93x + 1.08y = 115
We now have a system of two equations:
x + y = 12500
0.93x + 1.08y = 115
To solve this system, we can use the method of substitution. Rearrange the first equation to solve for 'x':
x = 12500 - y
Now substitute this expression for 'x' into the second equation:
0.93(12500 - y) + 1.08y = 115
Simplify the equation:
11625 - 0.93y + 1.08y = 115
Combine like terms:
0.15y = 115 - 11625
0.15y = -11510
Divide both sides by 0.15:
y = -11510 / 0.15
y ≈ -76666.67
Since 'y' represents the amount invested at an 8% gain, it cannot be a negative value. There must be a mistake in the given information or calculations. Please double-check your numbers and calculations.
To solve this problem, let's assume Lydia invested x dollars at a 7% loss and (12500 - x) dollars at an 8% gain.
To calculate the net annual receipts, we need to find the sum of the earnings from both investments.
For the first investment, Lydia experienced a 7% loss, which means she received 93% (100% - 7%) of her investment.
So, the return from the first investment is x * 0.93.
For the second investment, Lydia earned an 8% gain, which means she received 108% (100% + 8%) of her investment.
So, the return from the second investment is (12500 - x) * 1.08.
Now, we can set up the equation:
x * 0.93 + (12500 - x) * 1.08 = 115
Simplifying the equation:
0.93x + 13500 - 1.08x = 115
-0.15x = -13385
x = -13385 / -0.15
x ≈ 89233.33
Therefore, Lydia invested approximately $89233.33 at a 7% loss, and the remaining amount of approximately $23266.67 (12500 - 89233.33) at an 8% gain.