Investment Problem
A woman invested in two business ventures. Last year she made a profit of 15 percent from the first venture but lost 5 percent from the second venture.

If last year's income from the two investments was equivalent to a return of 8 percent on the entire amount invested, how much had she invested in each venture?

Solution
In order to solve this problem, first we should define how much was the total profit or return of investment (ROI) last year using the statement written in blue above. Thus we have this derivation:

        I = last years income from the two investments
      I = (25,000)(8%)
        = (25,000)(0.08)
      I = 2000

Therefore, the woman earned a profit of $2,000 last year from her two business ventures. However, we now need to know how much she earned in each business venture. Thus, we have the following representation:

Let
        x = amount invested in the first venture
        25,000 - x = amount invested in the second venture
        I = (P)(R)

Hence,
        $I = x(0.15) - (25000 - x)(0.05)$
        $2000 = 0.15x - (1250 - 0.05x)$           

       (Since the second investment was a loss, the second term is negative)

        $2000 = 0.15x - 1250 + 0.05x$
        $2000 + 1250 = 0.2x$
        $3250 = 0.2x$
        $\frac{3250}{0.2} = x$
        $16250 = x$
and
        25000 - 16250 = 8750

Therefore, the woman invested $16,250 in the first venture and $8,750 in the second venture.

Check
Total investment was $25,000: 16,250 + 8,750 = 25,000
Income was $2,000: (16,250)(0.15) - (8,750)(0.05)
                                       2,437.5 - 437.5
                                       2,000