Question 985745
Let A and B be the two properties. We'll make property A be the property where he made a 15% profit. We'll make property B be the property where he made a 5% loss. 


Let
x = amount of money, in dollars, invested in property A
y = amount of money, in dollars, invested in property B


He only has 2 choices to invest in, and he has $25000 to invest, so the total (x+y) must equal 25000
The first equation is x+y = 25000. Solve for y to get 


x+y = 25000
x+y-x = 25000-x <font color="blue">Subtract x from both sides.</font>
y = 25000-x


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Property A
invested x dollars, got a 15% profit so the amount he got back was 1.15x (x+0.15x = 1.15x)


Property B
invested y dollars, got a 5% loss so the amount he got back was 0.95y (y-0.05y = 0.95y)


Total:
1.15x + 0.95y in combined returns
We're given the return is equivalent to 8% of the total amount invested ($25000), ie equivalent to 1.08*25000 = 27000
So the second equation is this 1.15x + 0.95y = 27000



Focus on the second equation. Replace y with 25000-x and solve for x


1.15x + 0.95y = 27000
1.15x + 0.95(25000-x) = 27000 <font color="blue">Replace y with 25000-x</font>
1.15x + 0.95(25000)+0.95(-x) = 27000 <font color="blue">Distribute</font>
1.15x +23750-0.95x = 27000
0.2x +23750 = 27000
0.2x +23750-23750 = 27000-23750 <font color="blue">Subtract 23750 from both sides.</font>
0.2x = 3250
0.2x/0.2 = 3250/0.2 <font color="blue">Divide both sides by 0.2 to isolate x.</font>
x = 16250


Now use this x value to find y


y = 25000-x
y = 25000-16250
y = 8750


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Answer:


The results for x and y were

x = 16250
y = 8750


The amount invested in property A (the property with 15% profit) was $16250
The amount invested in property B (the property with 5% loss) was $8750