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Algebra 1 : How to find the percent of increase

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Example Question #101 : How To Find The Percent Of Increase

A garbage collector is able to finish his daily route in 5 hours. The city decides to give him a larger route. Now his route takes 8 hours to complete. What is the percentage change in the amount of time his route takes him to complete?

Possible Answers:

$35\%$

$60\%$

$80\%$

$40\%$

$45\%$

Correct answer:

$60\%$

Explanation:

This is a simple percentage change problem. Use the formula new amount subtracted by old amount then divided by old amount and multiplied by 100.

$\frac{8-5}{5}\cdot 100$

$\frac{3}{5}\cdot 100$

$0.6\cdot 100$

$60\%$

The amount of time the route takes the garbage collector increased by 60%

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Example Question #102 : How To Find The Percent Of Increase

A mattress company focuses on advertising and selling its king mattresses. The company makes a profit of $645,000 in the year. The CEO realizes that by focusing on increasing sales of queen and full size mattresses the company can attract more customers and boost sales. In the next year, the company makes a profit of $870,000. What is the percent change in the amount of profit the company makes by switching to a focus on queen and full size mattresses? (Round to one decimal place)

Possible Answers:

$36.2\%$

$22.8\%$

$28\%$

$41.3\%$

$34.9\%$

Correct answer:

$34.9\%$

Explanation:

Use the formula new amount subtract by old amount then divided by old amount and multiplied by 100. The new amount is $870,000 and the old amount is $645,000. The formula should look like this

$\frac{870000-645000}{645000}\cdot 100$

$\frac{225000}{645000}\cdot 100$

$0.3488\cdot 100$

$34.88\%$

$34.9\%$

The company's profits increased by 34.9% from the previous year.

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Example Question #103 : How To Find The Percent Of Increase

The theatrical version of a movie runs for a length of 2 hours and 20 minutes. When the movie is released for home viewing on DVD and Blu Ray it includes deleted scenes that increase its run time to 3 hours and 10 minutes. What is the percentage change of going from the theatrical version to the home release? (Round to one decimal place)

Possible Answers:

$19.6\%$

$26.5\%$

$28.8\%$

$42.4\%$

$35.7\%$

Correct answer:

$35.7\%$

Explanation:

This question requires putting the two times in similar units, which means either both in hours or both in minutes. It is easier to put both times in minutes. Since 60 minutes are in an hour, multiply 60 by the hours for each unit and add it to the number of minutes.

For 2 hours 20 minutes

2*60+20

120+20

140 minutes

For 3 hours 10 minutes

3*60+10

180+10

190 minutes

Now use the percent change formula new amount subtracted by old amount then divided by the old amount and multiplied by 100. 2 hours and 20 minutes is the old amount and 3 hours and 10 minutes is the new amount.

$\frac{190-140}{140}\cdot 100$

$\frac{50}{140}\cdot 100$

$0.3571\cdot 100$

$35.71\%$

$35.7\%$

This means that the home release version was 35.7% longer than the theatrical version.

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Example Question #104 : How To Find The Percent Of Increase

Last month at work, you earned $10 an hour. This month, you now earn $12.50 an hour. Find the percent increase in pay.

Possible Answers:

$2.5\%$

$30\%$

$25\%$

$15\%$

$20\%$

Correct answer:

$25\%$

Explanation:

To find percent increase, we use the following formula:

$\text{percent increase} = \frac{\text{new price - original price}}{\text{original price}} \cdot 100$

Using the information given, we know the following:

$\text{new price} = \$12.50$

$\text{original price} = \$10.00$

so we can substitute these values into the formula. We get

$\text{percent increase} = \frac{\$12.50 - \$10.00}{\$10.00} \cdot 100$

$\text{percent increase} = \frac{\$2.50}{\$10.00} \cdot 100$

$\text{percent increase} = 0.25 \cdot 100$

$\text{percent increase} = 25$

Therefore, the percent increase in price is $25\%$ .

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Example Question #105 : How To Find The Percent Of Increase

Last week, a pound of apples cost $5. This week, a pound of apples cost $6. Find the percent of increase in the cost of apples.

Possible Answers:

$10\%$

$20\%$

$1\%$

$15\%$

$6\%$

Correct answer:

$20\%$

Explanation:

To find percent increase, we use the following formula:

$\text{percent increase} = \frac{\text{new price - original price}}{\text{original price}} \cdot 100$

Using the information given, we know the following:

$\text{new price} = \$6.00$

$\text{original price} = \$5.00$

so we can substitute these values into the formula. We get

$\text{percent increase} = \frac{\$6.00 - \$5.00}{\$5.00} \cdot 100$

$\text{percent increase} = \frac{\$1.00}{\$5.00} \cdot 100$

$\text{percent increase} = 0.20 \cdot 100$

$\text{percent increase} = 20\%$

Therefore, the percent increase in price is $20\%$ .

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Example Question #106 : How To Find The Percent Of Increase

A professional baseball team wins 31 games in their first season, 50 games in their second season, and 94 wins in their third season. What is the percentage change from the team's first season to their third season? (Round to one decimal place)

Possible Answers:

$148.6\%$

$203.2\%$

$88\%$

$170\%$

$120.6\%$

Correct answer:

$203.2\%$

Explanation:

The inclusion of the second season win number is a trick. Use the percent change formula of new amount subtracted by old amount then divided by old amount and multiplied by 100 with 94 as the new amount and 31 as the old amount.

$\frac{94-31}{31}\cdot100$

$\frac{63}{31}\cdot100$

$2.0322\cdot100$

$203.22\%$

$203.2\%$

From the first season to the third season, the team's amount of wins increased by 203.2%

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Example Question #107 : How To Find The Percent Of Increase

In 2012, a pizza parlor sold 13750 pizzas. In 2011, the same pizza parlor sold 12500 pizzas in a year. What is the percent increase in the amount of pizzas the pizza parlor sold?

Possible Answers:

$15\%$

$10\%$

$7.25\%$

$13\%$

$12.5\%$

Correct answer:

$10\%$

Explanation:

Usually when you are doing a percent change problem, you take the new amount subtracted by the old amount, then divide by the old amount, and then convert the decimal to a percentage by multiplying by 100. The important aspect to these problems once you know the formula is to recognize the numbers as either new or old.

In this problem, 2011 is the first year mentioned so the amount of pizzas sold that year should be the old amount, 12500. The 2012 amount of pizzas is the new amount, 13750.

The set up of the formula is

$\frac{13750-12500}{12500}\cdot 100$

$\frac{1250}{12500}\cdot 100$

$0.1\cdot 100$

$10\%$

This represents a 10% increase in the amount of pizzas sold from 2011 to 2012.

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Example Question #108 : How To Find The Percent Of Increase

Last year, a school had 351 enrolled students. This year, enrollment at the same school was up to 387 students. By what percentage did enrollment increase (to two decimal places)?

Possible Answers:

0.10

10.25

9.30

102.5

Cannot determine from information given

Correct answer:

10.25

Explanation:

Find the increase in students in nominal terms (below, in the numerator) and divide that by the base, which is the number of students in the first year.

$\frac{387-351}{351} = \frac{36}{351}=0.1025$

Multiply the result from above by 100 to get the percent increase.

$0.1025 \times 100 = 10.25$ %

Note: to get the final answer to two decimal places, carry at least 4 decimal places from the first step of the calculation.

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Algebra 1 : How to find the percent of increase

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #101 : How To Find The Percent Of Increase

Example Question #102 : How To Find The Percent Of Increase

Example Question #103 : How To Find The Percent Of Increase

Example Question #104 : How To Find The Percent Of Increase

Example Question #105 : How To Find The Percent Of Increase

Example Question #106 : How To Find The Percent Of Increase

Example Question #107 : How To Find The Percent Of Increase

Example Question #108 : How To Find The Percent Of Increase

All Algebra 1 Resources

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