Math CentralQuandaries & Queries


Question from Mary:

$\$96$ is 66 2/3% of what dollar amount?

Hi Mary,

The structure of the English sentence can tell you a lot but first let's deal with 66 2/3%. The fraction 2/3 is 0.666 with the 6 repeating so 66 2/3 is approximately 66.667. But percent means per 100 20

\[66 \frac23\% = 66.667\% = \frac{66.667}{100} = 0.66667\]

Back to the English sentence which is now

$\$96$ is 0.6667 of what dollar amount?

The word "is" in the above sentence could be replaced by "is equal to" which is written = in mathematical notation. Thus the sentence could be written

$\$96$ = 0.6667 of what dollar amount?

What about the word "of"? we know that half of 100 is 50, one quarter of 20 is 5 and two thirds of nine is 6 so it looks like "of" is multiplication. Thus, finally the sentence is


$\$96 = 0.6667 \times \mbox{ (what dollar amount)}?$

I put the parentheses around "what dollar amount" because it's one value and in algebra we usually express such a quantity with a letter, for example $x.$ Thus we have

$\$96 = 0.6667 \times x.$

Can you solve for $x?$ Make sure you verify your answer.


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