Answer This Linear Equation Thanks..?

Question

1.) A retail merchant invested $6500 in three kinds of cameras. the profit on the sales of camera A was 25 percent; on the sales of camera B was 12 percent; and there was a loss of 1 percent on the sales of camera C.If the merchant invested equal amount in cameras A and B, and the overall profit on the total sales 14 percent,how much was invested in each kind of camera?

2.)A woman invested $25,000 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 town the two investments was equivalent to a return of 8 percent on the entire amount invested,how much she invested in each venture?

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Answer 1

1)

Money invested in camera A: invA

Money invested in camera B: invB

Money invested in camera C: invC

Total money invested: $6500 = invA + invB + invC

Since invA = invB: $6500 = 2 * invA + invC  (equation 1)

camera A's profit: 0.25 * invA

camera B's profit: 0.12 * invB = 0.12 * invA

camera C's profit: -0.01 * invC

Total profit: 0.14 * $6500 = $910 = 0.25 * invA + 0.12 * invA - 0.01 * invC = 0.37 * invA - 0.01 * invC  (equation 2)

Now solve for invA in one equation and insert it into the other to get the result, which is: invC = $1500.

2)

Money invested in venture 1: vent1

Money invested in venture 2: vent2

Total money invested: $25000 = vent1 + vent2  (equation 1)

venture 1's profit: 0.15 * vent1

venture 2's profit: -0.05 * vent2

Total profit: 0.15 * vent1 - 0.05 * vent2 = 0.08 * $25000 = $2000  (equation 2)

Now solve for either venture and put it in the other equation to get the results:

vent1 = $16250

vent2 = $8750

It is most important to realize what information you are given.  You are always given equations encoded in sentences.  Decode them, write down the equations, and combine them to get the results.

Answer 2

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