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This question has the following situation: "A motorcycle importer is planning on increasing the price of a certain model by $1,000. At this new price 5 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?"
(A) 51
(B) 61
(C) 66
(D) 71
(E) 76
The correct answer is C, and the solution used "back-solving" by plugging in the random number to verify the answer. The part that confuses me is representing this situation with two variables and two unknowns.
Here is how I presented the situation:
Revenue "R" = Sales "S" X Price "P"
Old revenue: $594,000 - $26,000 = $568,000 = S X P
New revenue: $594,000 = (S - 5) X (P + 1,000)
Here is how the book presented the situation:
Old revenue: $568,000 = (S + 5) X (P - 1,000)
New revenue: $594,000 = S X P
By following the solution, back-solving makes the first equation irrelevant because we're substituting values of "S" to the second equation and verifying if the result is the old revenue. Could you explain where I went wrong with my use of two variables two unknowns in order to illustrate the situation?
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