SOLUTION: Les invested a total of $25000 in two pieces of property last year. He made a profit of 15% on one lot but lost 5% on the second lot. If the profit was equivalent to a return of 8%

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Question 985745: Les invested a total of $25000 in two pieces of property last year. He made a profit of 15% on one lot but lost 5% on the second lot. If the profit was equivalent to a return of 8% on the total investment, how much was invested in each lot?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 Subtract x from both sides.
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 Replace y with 25000-x
1.15x + 0.95(25000)+0.95(-x) = 27000 Distribute
1.15x +23750-0.95x = 27000
0.2x +23750 = 27000
0.2x +23750-23750 = 27000-23750 Subtract 23750 from both sides.
0.2x = 3250
0.2x/0.2 = 3250/0.2 Divide both sides by 0.2 to isolate x.
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