a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the 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?  Choose the correct choice from the following choices
A) 8 % B) 15 % C) 45 % D) 52 % E) 67 %
<gadget id="calculator">5 / 20</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>

<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">25 - (25/3)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) / 25</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>

<result>E</result>
a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the 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?
multiply(divide(subtract(multiply(divide(5, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(5, 20), const_100)), const_100)
solution : 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 = 5 / 20 = 1 / 4 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 percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 1 – 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than ½ , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e .