Heather solved this problem:

Question

75 is 300% of what number?

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 300 Over 100 EndFraction = StartFraction 75 Over question mark EndFraction. StartFraction part Over whole EndFraction = StartFraction 75 times 4 Over 100 times 4 EndFraction = StartFraction 300 Over 400 EndFraction

What error did Heather make?
None. Her work is correct.
She multiplied 75 and 4 incorrectly.
She should have divided 75 by 4, and divided 100 by 4.
She used the part, 75, to write the percent ratio. The part-to-whole percent ratio is StartFraction 300 Over 100 EndFraction

Answer 1

Heather made an error in her work. The correct interpretation of the problem "75 is 300% of what number?" involves understanding the relationship between part, whole, and percentage.

When solving "75 is 300% of what number?" you should set it up as follows:

• Let \( x \) be the unknown number.

• Since 300% can be written as \( \frac{300}{100} = 3 \), we can express the relationship as:

  \( 75 = 3 \times x \)

To find \( x \), you would divide both sides by 3:

\( x = \frac{75}{3} = 25 \)

In Heather's work, she incorrectly set up the ratio and conflated the part-to-whole relationships. Therefore, the correct critique of her work is:

She used the part, 75, to write the percent ratio. The part-to-whole percent ratio is \(\frac{300}{100}\).