Explanation

Because no actual amounts of money are stated in the question, use smart numbers to solve this problem. If Mary has half as many cents as Nora has dollars, then, as an example, if Nora had $10, Mary would have 5 cents. Nora’s $10 equals 1,000 cents. To determine what percent more cents Nora has, use the percent change formula:

Percent Change=\((\frac{Difference}{original} \times 100)\)

Percent Change=\((\frac{1000-5}{5} \times 100)=19900\%\)

Any example in which “Mary has half as many cents as Nora has dollars” will yield the same result. Note that the percent change formula is required—a percent more (or percent increase) is not the same as a percent of something.


To do the problem algebraically (which is more difficult than using a smart number, as above), use M for Mary’s cents and N for Nora’s cents. Divide N by 100 in order to convert from cents to dollars, \(\frac{N}{100}\), and set up an equation to reflect that Mary has half as many cents as Nora has dollars:

\(M= \frac{1}{2} (\frac{N}{100})\)

\(M=\frac{N}{200}\)

\(200M=N\)

Therefore, Nora has 200 times as many cents. 200 times as many is 199 times more. To convert 199 times more to a percent, add two zeros to get 19,900%.