Bunuel wrote:

Adam originally acquired a identical rare coins for 1,000 dollars each. Suppose the price at which he sells each coin is 5000 – 20a, what is his total profit?

A. 4,000 – 19a

B. 4,000 – 20a^2

C. 4,000a – 20a^2

D. 4,000 - 20a

E. 5,000 - 1,020a

The twist in this problem: quantity

a just happens to be part of calculating the sell price. Sell price still has to be multiplied by quantity

a to get total revenue.

AlgebraTotal cost: (cost per coin)*(# of coins) = 1,000a

Total revenue: (price per coin)*(# of coins)

(5,000 - 20a)*(a) = 5,000a - 20a\(^2\)

Total profit: Total revenue - total cost

(5,000a - 20a\(^2\)) - 1,000a

5,000a - 20a\(^2\) - 1,000a

4,000a - 20a\(^2\)

Answer C

Assign valuesThis question is not very amenable to assigning values. If you use a = 1, e.g., answers B, C, D, and E will work.

Nonetheless, if you are stuck on the algebra, use a round number. (20a is a clue. A round number there is good, as is a round number when 5,000 - 20a is multiplied by "a.")

Let a = 10

Total cost of 10 coins, in $, at 1,000 per coin = 10,000

Sell price, in $:

5,000 - (20)(10) = 5,000 - 200 = 4,800 per coin

Total revenue: (4,800)*10 = 48,000

Profit = Total revenue - total cost

48,000 - 10,000 = 38,000

With a = 10, find the answer choice that yields 38,000

Eliminate A, B, D, and E

Their starting number (4,000 or 5,000) is much less than $38,000, let alone after some amount has been subtracted.

By process of elimination, the answer is C.

Check: 4,000a – 20a\(^2\)

(4,000)(10) - (20)(10\(^2\))

40,000 - (20)(100)

40,000 - 2,000 = 38,000 MATCH

Answer C

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