Question

Write and solve a proportion to answer the question.

25% of what number $w$ is 9?

$=\frac{25}{100}$

Answer 1

• 9/w = 25/100
• w = 36

Explanation:

You want the proportion and its solution that represents the question, "25% of what number is 9?"

Proportion

The problem statement is telling us the ratio of 9 to w is 25%:

`(9)/(w)=(25)/(100)\\\\9*100=25* w\qquad\text{multiply by $100w$}\\\\w=(9*100)/(25)=36\qquad\text{divide by 25}`

The number is 36.

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Additional comment

We like to write these problems using the exact relation given:

"25% of w is 9"

0.25w = 9 . . . . . . . . . . . using math symbols

w = 9/0.25 = 36 . . . . . . solve this one-step equation

The "cross multiplication" step used above inevitably results in multiplying the variable by a number, then dividing by that number. That seems unnecessary.