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Three Varieties of Percent Word Problems Study Guide (page 3)

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Updated on Oct 5, 2011

Three Varieties of Percent Word Problems Sample Questions

1. Ninety percent of the 300 dentists surveyed recommended sugarless gum for their patients who chew gum. How many dentists did NOT recommend sugarless gum?
2. The quality control step at the Light Bright Company has found that 2 out of every 1,000 light bulbs tested are defective. Assuming that this batch is indicative of all the light bulbs they manufacture, what percent of the manufactured light bulbs is defective?
3. The combined city and state sales tax in Bay City is. The Bay City Boutique collected \$600 in sales tax for sales on May 1. What was the total sales figure for that day, excluding sales tax?

Solutions to Sample Questions

Question 1

There are two ways to solve this problem.

Method 1:

Calculate the number of dentists who recommended sugarless gum using the technique, and then subtract that number from the total number of dentists surveyed to get the number of dentists who did NOT recommend sugarless gum.

 1. The of number is 300, and the % is 90: 2. Cross multiply and solve for is: is × 100 = 300 × 90 is × 100 = 27,000 Thus, 270 dentists recommended sugarless gum. 270 × 100 = 27,000 3. Subtract the number of dentists who recommended sugarless gum from the number of dentists surveyed to get the number of dentists who did NOT recommend sugarless gum: 300 – 270 = 30

Method 2:

Subtract the percent of dentists who recommended sugarless gum from 100% (reflecting the percent of dentists surveyed) to get the percent of dentists who did NOT recommend sugarless gum. Then, use the technique to calculate the number of dentists who did NOT recommend sugarless gum.

 1. Calculate the % of dentists who did NOT recommend sugarless gum: 100% – 90% = 10% 2. The of number is 300, and the % is 10: 3. Cross multiply and solve for is: is × 100 = 300 × 10 is × 100 = 3,000
 Thus, 30 dentists did NOT recommend sugarless gum. 30 × 100 = 3,000

Question 2

 1. 2 is the is number, and 1,000 is the of number: = 2. Cross multiply and solve for %: 2 × 100 = 1,000 × % 200 = 1,000 × %
 Thus, 0.2% of the light bulbs are assumed to be defective. 200 = 1,000 × 0.2

Question 3

1. Since this question includes neither the word is nor of, you have to put your thinking cap on to determine whether 600 is the is number or the of number! Since \$600 is equivalent to % tax, we can conclude that it is the part. The question is asking this: "\$600 tax is % of what dollar amount of sales?"

Thus, 600 is the is number, and is the %:  =

2. Cross multiply and solve for the of number: 600 × 100 = of ×

60,000 = of ×

You have to divide both sides of the equation by to get the answer:  60,000 – = of × ÷

7,058.82 of

Thus, \$600 is % of approximately \$7,058.82 (rounded to the nearest cent), the total sales on May 1, excluding sales tax.

Find practice problems and solutions for these concepts at Three Varieties of Percent Word Problems Practice Questions.

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