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
_________________
SC Butler has resumed! Get
two SC questions to practice, whose links you can find by date,
here.Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver