On 2 investments totaling 15,00, peter lost 2% on one and earned 8% on the other. If his annual receipts were $204, how much was each investment?
-.02x + .08(15000-x) = 204.00
x = 9960.00
check:
8% of 5040 = 403.20
2% of 9960 = 199.20
subtract: 204.00
Let's assume the amount invested at a 2% loss is x dollars.
So, the amount invested at an 8% gain would be (1500 - x) dollars.
According to the given information:
- The loss on the first investment is 2%, which means Peter lost 2% of x dollars.
- The gain on the second investment is 8%, which means Peter earned 8% of (1500 - x) dollars.
To calculate the actual values, we need to use percentages as decimals. So, 2% is equal to 0.02, and 8% is equal to 0.08.
Using the above information, we can write the following equation based on Peter's annual receipts:
0.02x + 0.08(1500 - x) = 204
Let's solve the equation to find the values of x and (1500 - x).
0.02x + 0.08(1500 - x) = 204
0.02x + 120 - 0.08x = 204
0.02x - 0.08x = 204 - 120
-0.06x = -84
x = -84 / -0.06
x = 1400
The amount invested at a 2% loss is $1400.
Therefore, the amount invested at an 8% gain is (1500 - 1400) = $100.
To find the amount of each investment, let's represent the amount Peter invested in the first investment as x dollars and the amount he invested in the second investment as y dollars.
We know the total amount Peter invested is 1500 dollars, so we can create an equation: x + y = 1500.
Now, let's calculate Peter's losses and earnings. He lost 2% on one investment and earned 8% on the other.
The loss on the first investment is 2% of x, which can be represented as (2/100)x or 0.02x.
The earnings on the second investment is 8% of y, which can be represented as (8/100)y or 0.08y.
Based on the given information, Peter's losses and earnings add up to $204. We can express this as an equation: 0.02x + 0.08y = 204.
Now we have a system of two equations:
x + y = 1500 (Equation 1)
0.02x + 0.08y = 204 (Equation 2)
We can solve this system of equations to find the values of x and y.
First, let's multiply Equation 1 by 0.02 to make the coefficients of x in both equations the same:
0.02x + 0.02y = 30 (Equation 3)
Now, let's subtract Equation 3 from Equation 2 to eliminate the x terms:
0.02x + 0.08y - (0.02x + 0.02y) = 204 - 30
0.08y - 0.02y = 174
0.06y = 174
Dividing both sides of the equation by 0.06, we get:
y = 174 / 0.06
y = 2900
Now we can substitute the value of y back into Equation 1 to find the value of x:
x + 2900 = 1500
x = 1500 - 2900
x = -1400
Since it doesn't make sense for an investment to be a negative value, we can conclude that there was an error in the question or our calculations.
Please double-check the given information and the calculations to ensure accuracy.