Algebra 1 : How to find the percent of increase

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #61 : How To Find The Percent Of Increase

Find the percent increase from \(\displaystyle 23\) to \(\displaystyle 28\)

Possible Answers:

\(\displaystyle \approx 22\%\)

\(\displaystyle \approx 12\%\)

\(\displaystyle \approx 52\%\)

\(\displaystyle \approx 32\%\)

Correct answer:

\(\displaystyle \approx 22\%\)

Explanation:

For this type of problem we use this formula: \(\displaystyle \frac{difference}{original} \times 100\). "Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows: \(\displaystyle \frac{28-23}{23}\times 100 = \frac {5}{23}\times 100 \approx 22\%\). This is our percent increase. 

Example Question #61 : How To Find The Percent Of Increase

Find the percent increase from \(\displaystyle 20\) to \(\displaystyle 35\)

Possible Answers:

\(\displaystyle 75\%\)

\(\displaystyle 87\%\)

\(\displaystyle 35\%\)

\(\displaystyle 64\%\)

Correct answer:

\(\displaystyle 75\%\)

Explanation:

For this type of problem we use this formula: \(\displaystyle \frac{difference}{original} \times 100\). "Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows: \(\displaystyle \frac{35-20}{20}\times 100 = \frac {15}{20}\times 100 = 75\%\). This is our percent increase. 

Example Question #61 : How To Find The Percent Of Increase

Find the percent increase from \(\displaystyle 20\) to \(\displaystyle 23\)

Possible Answers:

\(\displaystyle 135\%\)

\(\displaystyle 24\%\)

\(\displaystyle 13\%\)

\(\displaystyle 15\%\)

Correct answer:

\(\displaystyle 15\%\)

Explanation:

For this type of problem we use this formula: \(\displaystyle \frac{difference}{original} \times 100\). "Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows: \(\displaystyle \frac{23-20}{20}\times 100 = \frac {3}{20}\times 100 = 15\%\). This is our percent increase. 

Example Question #62 : How To Find The Percent Of Increase

Find the percent increase from \(\displaystyle 20\) to \(\displaystyle 21.5\)

Possible Answers:

\(\displaystyle 6.5\%\)

\(\displaystyle 4.5\%\)

\(\displaystyle 8.5\%\)

\(\displaystyle 7.5\%\)

Correct answer:

\(\displaystyle 7.5\%\)

Explanation:

For this type of problem we use this formula: \(\displaystyle \frac{difference}{original} \times 100\). "Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows: \(\displaystyle \frac{21.5-20}{20}\times 100 = \frac {1.5}{20}\times 100 = 7.5\%\). This is our percent increase. 

Example Question #65 : How To Find The Percent Of Increase

From 2014 to 2015, the price of a popular pair of sneakers rose from \(\displaystyle \$90\) to \(\displaystyle \$103\). What is the percent increase in the price of the sneakers? Please round your final percentage answer to one decimal place. 

Possible Answers:

\(\displaystyle 12.6\%\)

\(\displaystyle 21.4\%\)

\(\displaystyle 15.1\%\)

\(\displaystyle 17.2\%\)

\(\displaystyle 14.4\%\)

Correct answer:

\(\displaystyle 14.4\%\)

Explanation:

To find the percent increase, follow these steps:

First, find the difference between the two values given:

\(\displaystyle \$103 - \$90 = \$13\)

Next, divide the difference in values by the original value:

\(\displaystyle \$13 \div \$90 = .144\)

 

Finally, multiply this decimal by one-hundred to find its percentage equivalent:

\(\displaystyle .144 \times 100 = 14.4\%\)

Example Question #61 : Percent Of Change

You have a resting heart heart rate of 60 BPM. After 5 minutes of exercise your heart rate has increased by 85%. What is your heart rate at this time?

Possible Answers:

123 BPM

95 BPM

140 BPM

None of these answers.

111 BPM

Correct answer:

111 BPM

Explanation:

If your resting heart rate is 60 BPM and your heart rate increased by 85%, then your heart rate has increased by 85% of 60. Percentages are all relative. 85% means nothing unless it is 85% of something. The total heart rate then would be the sum of 60 and 85% of 60.

Find how much 85% of 60 is:

\(\displaystyle .85*60=51\)

Add the increase to the resting heart rate:

\(\displaystyle 60+51=111 \hspace{1mm}BPM\)

Example Question #62 : Percent Of Change

Find the percent increase in price if the original cost of an item was $20 and the final cost was $36.

Possible Answers:

\(\displaystyle 80\%\)

\(\displaystyle 180\%\)

\(\displaystyle 72\%\)

\(\displaystyle 17\%\)

\(\displaystyle 27\%\)

Correct answer:

\(\displaystyle 80\%\)

Explanation:

To find the percent of increase, use the following formula:

\(\displaystyle percent\;change=\frac{new-old}{old}\)

\(\displaystyle percent\;change=\frac{36-20}{20}=\frac{16}{20}=\frac{4}{5}=0.8\)

Example Question #61 : How To Find The Percent Of Increase

If a major league baseball player buys a baseball bat for \(\displaystyle \$115\) and puts his autograph on it, its price goes up to \(\displaystyle \$225\). What is the increase in price expressed as a percent change? Round to the nearest percent.

 

Possible Answers:

\(\displaystyle 98\%\)

\(\displaystyle 95\%\)

\(\displaystyle 96\%\)

\(\displaystyle 94\%\)

\(\displaystyle 97\%\)

Correct answer:

\(\displaystyle 96\%\)

Explanation:

To find a percent change you need to find the increase or decrease amount and divide it by the original amount.

Original price was \(\displaystyle \$115\)

New price is \(\displaystyle \$225\)

Amount of increase was \(\displaystyle \$110\)

\(\displaystyle 110 / 115 = .95652174\)

Multiply that by \(\displaystyle 100\) to get it to a percent.

\(\displaystyle 95.65\)

Round it to the nearest percent would make it \(\displaystyle 96\%\)

Example Question #63 : How To Find The Percent Of Increase

Avian Influenza has resulted in egg prices worldwide and locally to skyrocket. In April, eggs were \(\displaystyle \$2.09\) at the supermarket and by May their price tag had swelled to \(\displaystyle \$3.58\). What is the percent increase in the price of a dozen of eggs from April to May?

Possible Answers:

\(\displaystyle 58\%\)

\(\displaystyle 71\%\)

\(\displaystyle 82\%\)

\(\displaystyle 42\%\)

\(\displaystyle 78\%\)

Correct answer:

\(\displaystyle 71\%\)

Explanation:

To find the percent increase of a dozen of eggs, we first must find the price difference between the April and May prices:

\(\displaystyle \$3.58-\$2.09=\$1.49\)

The next step is to divide the difference in price by the original price for eggs. When multiplied by \(\displaystyle 100\%\), we are given our percent increase:

\(\displaystyle \frac{\$1.49}{\$2.09}\cdot100\%\)

\(\displaystyle 0.71\cdot100\%=71\%\)

Example Question #70 : How To Find The Percent Of Increase

What is the percent increase from \(\displaystyle 10\) to \(\displaystyle 13\) ?

Possible Answers:

\(\displaystyle 20\%\)

\(\displaystyle 30\%\)

\(\displaystyle 40\%\)

\(\displaystyle 60\%\)

Correct answer:

\(\displaystyle 30\%\)

Explanation:

For this type of problem we use this formula: 

\(\displaystyle \frac{difference}{original} \times 100\) 

"Difference" is simply the difference between the two numbers given, and "original" is the number that is stated usually after the word "from" , example: from ____ to ____. In this problem our formula will be filled in as follows:

\(\displaystyle \frac{13-10}{10}\times 100 = \frac {3}{10}\times 100 = 30\%\)

This our percent increase. 

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