VJesus12 wrote:A pharmaceutical company received $3 million in royalties on the first $20 million in sales of generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
A. 8%
B. 15%
C. 45%
D. 52%
E. 56%
This is a percent decrease problem. We will use the formula percent change = (new - old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 3/20
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percentages.
First 20 Million
royalties/sales = (3/20) x 60 = 9
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 9 and 5 into our percent change formula:
(new - old)/old x 100
[(5 - 9)/9] x 100
-4/9 x 100
At this point we can stop and consider the answer choices. Since we know that 4/9 is just a bit less than ½, we know that -4/9 x 100 is an approximately 45% decrease.
Answer:
C
