SOLUTION: A woman invested P25,000 in two business ventures, last year she made a profit of 15% from the first venture but lost 5% from the second venture. if the last years income from the

Question 174786: A woman invested P25,000 in two business ventures, last year she made a profit of 15% from the first venture but lost 5% from the second venture. if the last years income from the two investments was equivalent to a return of 8% of the entire amount invested, how much had she invested in each venture?
Answer by actuary(112) (Show Source): You can put this solution on YOUR website!
First, what are the equations that describe the situation:
Let x be the amount invested in the first venture.
Let Y be the amount invested in the second venture.
So x + y = 25000 (#1) (I'll disregard including the "P" for pounds in the intermediate steps of my calculation)
.15x -.05y = .08*25000 (#2)(This equation describes the relationship between th ereturn on each of the two ventures and the return on the total amount invested.
.15x - .05 (25000 - x) = 2000 (Substituting for "y" based on equation #1) performing the multiplication
Simplify
.15x - 1250 +.05x = 2000
Rearrange the equation
.2x = 2000+1250 = 3250
So x = 3250/.2 = P16250
From equation #1, solve for y
y = 25000 - 16260 =P8750
Checking the results by substituting the answers into the equations
16250 + 8750 = 25000 (OK)
.15*16250 -.05*8750 = 2437.5 - 437.5 = 2000
25000*.08 = 2000 (OK)
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