Math CentralQuandaries & Queries


Question from Art, a student:

what percent of 85 is 17?

Hi Art.

I will show you how to solve this with another set of numbers. What percent of 64 is 16?

The important idea is that the ratios (fractions) are the same. A percentage is just a fraction. It literally means "per hundred". So 70% is 70 per 100 which is 70 100.

With algebra we use a letter to represent an unknown value.

Let P be the percentage that 16 is of 64.

Then we can write this as two fractions that equal each other:

Now we want to "solve" this equation for P. That means we must multiply both sides of the equation by 100:

This lets us cancel out the 100 in the denominator with the 100 we multiplied both sides of the equation by:

Finally, we can divide 16 by 64 and then multiply by 100 on the right hand side to find the answer.

So in this case 16 is 25% of 64.

Your question can be solved exactly the same way, Art.

Hope this helps,
Stephen La Rocque.



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