Question

a publishing company wants to increase the price of one of its books by 10%. research shows that this increase in price would decrease sales of the book by only 5%. by what percent would this change increase the money received though sales of this book?

Answer 1

Even without knowing exactly what to do in this problem solution, I'd immediately represent the price of the book by d and the number of books sold by n.

Then, increasing the selling price by 10% would result in the price 1.10x.

Suppose the book originally sells for d dollars and that n volumes are sold. The resulting revenue would be (d dollars per book)*(n books) = dn dollars.

Suppose that we now increase the price of the book by 10% and indicate the reduced sales volume by (1-0.05)n = 0.95n.

Then the revenue from selling this book at its increased price will be
(1.10d)(0.95n) = ?

Now please set up a ration:

Revenue when price has been increased
---------------------------------
Revenue before price was increased

Calculate the decimal fraction that represents the increase in revenue.