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Algebra 1 : Percent of Change

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Example Question #23 : How To Find The Percent Of Decrease

Last week, a case of water cost $4.00. This week, it is on sale for $3.00 a case. Find the percent decrease.

Possible Answers:

$10\%$

$50\%$

$15\%$

$25\%$

$12\%$

Correct answer:

$25\%$

Explanation:

To find the percent decrease, we will use the following formula:

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

$\text{percent decrease} = \frac{\$4.00 - \$3.00}{\$4.00} \cdot 100$

$\text{percent decrease} = \frac{\$1.00}{\$4.00} \cdot 100$

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

$\text{percent decrease} = 25\%$

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Example Question #24 : How To Find The Percent Of Decrease

Yesterday, chicken cost $4 a pound. Today, it costs $3.50 a pound. Find the percent decrease.

Possible Answers:

$50\%$

$10\%$

$12.5\%$

$15\%$

$25\%$

Correct answer:

$12.5\%$

Explanation:

To find the percent decrease, we will use the following formula:

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

$\text{percent decrease} = \frac{\$4.00 - \$3.50}{\$4.00} \cdot 100$

$\text{percent decrease} = \frac{\$0.50}{\$4.00} \cdot 100$

$\text{percent decrease} = 0.125 \cdot 100$

$\text{percent decrease} = 12.5\%$

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Example Question #25 : How To Find The Percent Of Decrease

Last week, a shirt cost $25. This week, it is on sale for $10. Find the percent decrease.

Possible Answers:

$50\%$

$65\%$

$60\%$

$70\%$

$55\%$

Correct answer:

$60\%$

Explanation:

To find the percent decrease, we use the following formula:

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

$\text{percent decrease} = \frac{\$25 - \$10}{\$25} \cdot 100$

$\text{percent decrease} = \frac{\$15}{\$25} \cdot 100$

$\text{percent decrease} = 0.60 \cdot 100$

$\text{percent decrease} = 60\%$

Therefore, the percent decrease of the shirt is 60%.

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Example Question #26 : How To Find The Percent Of Decrease

A tennis player won 25 of her 35 matches in the fall season. In the spring season, she won 23 of her 35 matches. What was the tennis player's percent change in the number of games she won from fall to spring?

Possible Answers:

$-6\%$

$-12\%$

$-10\%$

$-8\%$

$-4\%$

Correct answer:

$-8\%$

Explanation:

In this question, it is important to not be confused by the total amount of games number. Since the number of games is the same, you can just take the new amount of wins subtracted by the old amount of wins then divide by the old amount and multiply by 100.

$\frac{23-25}{25}\cdot 100$

$\frac{-2}{25}\cdot 100$

$-0.08\cdot 100$

$-8\%$

The amount of games the tennis player won decreased by 8% from the fall season to the spring season.

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Example Question #27 : How To Find The Percent Of Decrease

Your weekly allowance went from $40 to $30 a week. Find the percent decrease in your allowance.

Possible Answers:

$4\%$

$10\%$

$30\%$

$20\%$

$25\%$

Correct answer:

$25\%$

Explanation:

To find percent decrease, we use the following formula:

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

Using the information given, we know the following:

$\text{original price} = \$40.00$

$\text{new price} = \$30.00$

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

$\text{percent decrease} = \frac{\$40.00 - \$30.00}{\$40.00} \cdot 100$

$\text{percent decrease} = \frac{\$10.00}{\$40.00} \cdot 100$

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

$\text{percent decrease} = 25\%$

Therefore, the percent decrease in your allowance is $25\%$ .

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Example Question #28 : How To Find The Percent Of Decrease

In 2013, a water tower contained 950,000 gallons. By 2014, the tower only contained 860,000 gallons of water. What was the percentage change in the amount of water that the tower contained? (Round to one decimal place)

Possible Answers:

$-6\%$

$-13\%$

$-16\%$

$-9.5\%$

$-12\%$

Correct answer:

$-9.5\%$

Explanation:

Use the formula new amount subtracted by old amount then divided by the old amount and multiplied by 100. The new amount in this case is 860,000 and the old amount is 950,000.

$\frac{860000-950000}{950000}\cdot100$

$\frac{-90000}{950000}\cdot100$

$-0.0947\cdot100$

$-9.47\%$

$-9.5\%$

The amount of water in the tower decreased by 9.5%

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Example Question #29 : How To Find The Percent Of Decrease

When performing a Google search for "Lions" the amount of search results are 257 million. After refining the search to "African Lions" the amount of search results is 6.7 million. What is the percentage change by going from a search for "Lions" to "African Lions"? (Round the answer to one decimal place)

Possible Answers:

$-79.8\%$

$-88.2\%$

$-80.4\%$

$-97.4\%$

$-70.5\%$

Correct answer:

$-97.4\%$

Explanation:

The percent change formula new amount subtracted by old amount then divided by old amount and multiplied by 100 should be used for this problem. The new amount is 6.7 million and the old amount is 257 million. It is not necessary to use the expanded numbers 6,700,000 or 257,000,000 to work out the problem but it will also work.

$\frac{6.7-257}{257}\cdot100$

$\frac{-250.3}{257}\cdot100$

$-0.9739\cdot100$

$-97.39\%$

$-97.4\%$

By refining the search, the amount of search results fell by 97.4%

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Example Question #30 : How To Find The Percent Of Decrease

A closet contains 250 shoes. During spring cleaning, the owner decides to donate away 50 of those shoes. What is the percentage change in the amount of shoes the person owns?

Possible Answers:

$-80\%$

$-40\%$

$-30\%$

$-20\%$

$-60\%$

Correct answer:

$-20\%$

Explanation:

Use the percentage change formula new amount subtracted by old amount then divided by old amount and multiplied by 100. It is important in this question to realize what the new and old amount are. The old amount is 250 shoes. The new amount is 250 less the 50 shoes so 200. The formula should be

$\frac{200-250}{250}\cdot 100$

$\frac{-50}{250}\cdot 100$

$-0.2\cdot 100$

$-20\%$

The amount of shoes owned decreased by 20%.

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Example Question #2921 : Algebra 1

Simplify the expression

$\frac{(3x^{4})^{2}}{x^{3}}$

What is the exponent of in the simplified expression?

Possible Answers:

Correct answer:

Explanation:

Apply the properties of exponents as follows:

$\frac{(3x^{4})^{2}}{x^{3}}$

$= \frac{3^{2}(x^{4})^{2}}{x^{3}}$

$= \frac{9(x^{4 \cdot 2})}{x^{3}}$

$= \frac{9x^{8}}{x^{3}}$

$= 9x^{8-3}$

$= 9x^{5}$

5 is the correct choice.

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Algebra 1 : Percent of Change

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #23 : How To Find The Percent Of Decrease

Example Question #24 : How To Find The Percent Of Decrease

Example Question #25 : How To Find The Percent Of Decrease

Example Question #26 : How To Find The Percent Of Decrease

Example Question #27 : How To Find The Percent Of Decrease

Example Question #28 : How To Find The Percent Of Decrease

Example Question #29 : How To Find The Percent Of Decrease

Example Question #30 : How To Find The Percent Of Decrease

Example Question #2921 : Algebra 1

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