A technology company made a $5 million profit on its first $15 million in sales and a $12 million profit on its next $30 million in sales. By what percent did the ratio of profit to sales increase from the first $15 million in sales to the next $30 million in sales? Choose the correct choice from the following choices:
A) 10%  B) 20%  C) 30%  D) 40%  E) 50%
Solution:   This is a percent increase 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 profits to sales. The first ratio will be for the first 15 million in sales, and the second ratio will be for the next 30 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 15 Million   profit/sales = 5/15 =1/3   Next 30 Million   profit/sales = 12/30 = 2/5   We can simplify each ratio by multiplying each by the LCM of the two denominators, which is 15. Keep in mind that we are able to do this only because our answer choices are expressed in percents.   First 15 Million   royalties/sales = (1/3) x 15 = 5   Next 30 Million   royalties/sales = (2/5) x 15 = 6   We can plug 5 and 6 into our percent change formula:   (new – old)/old x 100   [(6 – 5)/5] x 100   1/5 x 100, so a 20% increase.   Answer 20%.
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A technology company made a $5 million profit on its first $15 million in sales and a $12 million profit on its next $30 million in sales. By what percent did the ratio of profit to sales increase from the first $15 million in sales to the next $30 million in sales?