Problem Solving

Mike@Magoosh wrote:An importer wants to purchase N high quality cameras from Germany and sell them in Japan. The cost in Germany of each camera is E euros. He will sell them in Japan at Y yen, which will bring in a profit, given that the exchange rate is C yen per euro. Given the exchange rate of D US dollars per euro, which of the following represents his profit in dollars?
(A) N(YC - DE)
(B) ND(YC - E)
(C) ND[(Y/C) - E]
(D) N[(Y/C) - DE]
(E) ND(Y - E)/C

Let N=1, implying that 1 camera is purchased.

Let E=1, implying that the cost of the 1 camera is 1 Euro.

Let C=2, implying that 2 Yen = 1 Euro and that the cost of the camera is 2 Yen.

Let Y=10, implying that the camera is sold for 10 Yen.

Thus:
Profit = (10 Yen) - (2 Yen) = 8 Yen = 4 Euro.

Let D=3, implying that 1 Euro = $3.
Thus, a profit of 4 Euro is equal to $12. This is our target.

Now plug N=1, E=1, C=2, Y=10, and D=3 into the answers to see which yields our target of 12.
Only C works:
ND[(Y/C) - E] = (1*3)(10/2 - 1) = 12.

The correct answer is C.

Cost of each camera in Germany is E euros

Selling price of each camera in Japan is Y yen, which is Y/C euros ( given that C yen per euro)

Profit per camera ( in euro) = Y/C - E
Profit for N cameras = N [ (Y/C) - E ]

now 1 euro = D $

so Profit for N camera in $ = DN [ (Y/C) - E ]

I hope its clear