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?"
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?