Last year, Company X spent $3 million to manufacture consumer goods th

These answers are far apart and the question says "approximately."
We do not need exact calculation.

(1) find ratio of manufacturing costs, \(C\), to sales revenues, \(R\), for last year and this year

Whenever possible in percent problems, get the denominator to 100 (and change the numerator accordingly).

Last year: \(\frac{C}{R}=\frac{3}{50}=\frac{6}{100}\)

This year: \(\frac{C}{R}=\frac{5}{98}\approx{\frac{5}{100}}\)

This year: The numerator is tiny. The denominator is close to 100. Use the approximation.

(2) Find percent change from last year's ratio to this year's ratio

"By approximately what percent did the ratio ... decrease" = find the percent change

Percent change (decrease) in the ratio = \(\frac{Change}{Original}=\frac{(New-Old)}{Old} *100\)

Percent change =

\(\frac{\frac{5}{100}-\frac{6}{100}}{\frac{6}{100}}=\frac{-\frac{1}{100}}{\frac{6}{100}}=(-\frac{1}{100}*\frac{100}{6})=-\frac{1}{6}*100\)

Percent change = \((-\frac{1}{6}*100)=(- .1667*100)\approx{-16.7}\) %

The minus sign = percent decrease. The ratio decreased by approximately \(16.7\) %

That answer* is much closer to 15% than it is to 25%

Answer C

**The answers are far enough apart that we do not need to worry about this issue, but that answer is too great. We should round our answer down. We used a smaller-than-actual ratio. (\(\frac{5}{100}\) is smaller than \(\frac{5}{98}\))
Use easy numbers to verify. \(\frac{12-4}{4} = 2\) BUT \(\frac{16-4}{4} = 3\). Greater dividend = smaller answer.