On two investments totaling 13,000 brain lost 6% on one and earned 9% on the other if his net annual receipts were 189 how much was each investment
Let's assume the amount of money invested at a 6% loss is x, and the amount of money invested at a 9% gain is y.
We can set up two equations based on the given information:
1) 0.06x - 0.09y = -189 (the 6% loss is negative while the 9% gain is positive)
2) x + y = 13,000 (total investments equal 13,000)
To solve this system of equations, we can use the substitution method.
From equation 2), we can solve for x in terms of y:
x = 13,000 - y
Substituting this expression for x into equation 1), we have:
0.06(13,000 - y) - 0.09y = -189
780 - 0.06y - 0.09y = -189
-0.15y = -969
y = (-969) / (-0.15)
y = 6,460
Now that we have the value of y, we can substitute it back into equation 2) to solve for x:
x + 6,460 = 13,000
x = 13,000 - 6,460
x = 6,540
Therefore, the amount invested at a 6% loss is $6,540, and the amount invested at a 9% gain is $6,460.