Algebra 1 : Percent of Change

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #2811 : Algebra 1

Find the percent increase from \displaystyle 56 to \displaystyle 79

Possible Answers:

\displaystyle \small 43\%

\displaystyle \small 41\%

\displaystyle \small 39\%

\displaystyle \small 23\%

\displaystyle \small 40\%

Correct answer:

\displaystyle \small 41\%

Explanation:

To find the percent of increase from one number to the next simply use this formula, 

\displaystyle \small \frac{difference}{original} \times100.

In this problem, our "difference" is just \displaystyle \small 79-56 = 23.

Next, we place that difference over our original, \displaystyle \small \frac{23}{56}, and then multiply against \displaystyle \small 100 in order to convert out answer to a percentage, resulting in about \displaystyle \small 41.07\%\displaystyle \small \approx41\%

Example Question #21 : How To Find The Percent Of Increase

Mark's income over the past year has gone up \displaystyle 20\%. It is now \displaystyle \$21 per hour. What was his hourly income before the raise?

Possible Answers:

\displaystyle \$12

\displaystyle \$16

\displaystyle \$14

\displaystyle \$18

\displaystyle \$17.50

Correct answer:

\displaystyle \$17.50

Explanation:

To find the original value, use the following relation.

\displaystyle \frac{new-old}{old}*100=percentage

We know the percentage, and we know the new value, so we can solve for the old value.

\displaystyle \frac{21-old}{old}=.2

\displaystyle 21-old=.2old

\displaystyle 21=1.2old

\displaystyle old=\frac{21}{1.2}=17.5

 

Example Question #21 : How To Find The Percent Of Increase

What is the percent change from \displaystyle \small 239 to \displaystyle \small 489 ? 

Possible Answers:

\displaystyle \small \approx96\%

\displaystyle \small 97\%

\displaystyle \small 29\%

\displaystyle \small \approx 104.6\%

Correct answer:

\displaystyle \small \approx 104.6\%

Explanation:

To find the percent change we use the formula 

\displaystyle \small \frac{difference}{original} \times 100.

In this problem, we are asked to find the percent increase from \displaystyle \small 239 to \displaystyle \small 489.

So our formula will look like this: 

\displaystyle \small \frac{250}{239} \times 100 = 104.6.

Thus, the percent increase from \displaystyle \small 239 to \displaystyle \small 489 is about \displaystyle \small 104.6\%

Example Question #2812 : Algebra 1

What is the percent increase from \displaystyle \small 389 to \displaystyle \small 589?

Possible Answers:

\displaystyle \small \approx 91\%

\displaystyle \small 2\%

\displaystyle \small \approx 51\%

\displaystyle \small \approx 71\%

Correct answer:

\displaystyle \small \approx 51\%

Explanation:

To find the percent increase from one number to the next, the first step is to find the difference between the two numbers given, \displaystyle \small 589-389 = 200.

The formula we use to solve this type of equation is: 

\displaystyle \small \frac{difference}{original} \times 100..

Our original number here is \displaystyle \small 389., so our formula: 

\displaystyle \small \frac{200}{389}\times 100 \approx51.4\%. 

This means that from \displaystyle \small 389 to \displaystyle \small 589, we had to add about \displaystyle \small 51.4\% of \displaystyle \small 389 to \displaystyle \small 389 to get \displaystyle \small 589.

Example Question #22 : How To Find The Percent Of Increase

What is the percent of increase from \displaystyle \small 18982 to \displaystyle \small 21834?

Possible Answers:

\displaystyle \small \approx 25\%

\displaystyle \small \approx 17\%

\displaystyle \small \approx 15\%

\displaystyle \small \approx 19\%

Correct answer:

\displaystyle \small \approx 15\%

Explanation:

To find the percent of increase from \displaystyle \small 18982 to \displaystyle \small 21834 we first must find the range between the numbers, 

\displaystyle \small 21834-18982 = 2852.

Then we use this formula to find the percent increase: 

\displaystyle \small \frac{difference}{original}\times 100.

For this data given, 

\displaystyle \small \small \frac{2852}{18982} \times 100 \approx 15\%

Example Question #21 : How To Find The Percent Of Increase

Find the percent change.

The cost of a phone went from \displaystyle \$450 to \displaystyle \$399. What is the percent of change of the phone?

Possible Answers:

\displaystyle 25\%

\displaystyle 11.33\%

\displaystyle 88.67\%

\displaystyle 188.67\%

\displaystyle 12.78\%

Correct answer:

\displaystyle 11.33\%

Explanation:

To find the percent change of the phone we will need to use the following formula.

\displaystyle percent\:of \: change=\left | \frac{new-old}{old}\right |\ast100

Applying our values 

\displaystyle old=\$450

\displaystyle new=\$399

to the percent change formula we find,

\displaystyle percent\:of \: change=\left | \frac{399-450}{450}\right |\ast100=11.33\%

                                    

Example Question #26 : Percent Of Change

Find the percent of increase from \displaystyle 12 to \displaystyle 15

Possible Answers:

\displaystyle \small 25\%

\displaystyle \small 35\%

\displaystyle \small 37\%

\displaystyle \small 14\%

Correct answer:

\displaystyle \small 25\%

Explanation:

To find the percent of increase from one number to the next, this formula is used: 

\displaystyle \small \frac{difference}{original} \times 100.

The numerator in this case would be 

\displaystyle \small 15-12=3.

So our formula would be 

\displaystyle \small \frac{3}{12}\times 100 = 25\%.

It is a \displaystyle \small 25\% increase from \displaystyle \small 12 to \displaystyle \small 15.

Example Question #22 : Percent Of Change

Find the percent increase from \displaystyle \small 100 to \displaystyle \small 124

Possible Answers:

\displaystyle \small 29\%

\displaystyle \small 94\%

\displaystyle \small 44\%

\displaystyle \small 24\%

Correct answer:

\displaystyle \small 24\%

Explanation:

To find the percent increase from \displaystyle \small 100 to \displaystyle 124, we first recognize that the formula needing to be used is 

\displaystyle \small \frac{difference}{original}\times100.

The difference here is, 

\displaystyle \small 124-100=24,

meaning our formula will look like this: 

\displaystyle \small \frac{24}{100}\times 100 = 24\%.

This, then, is our percent increase. 

Example Question #23 : Percent Of Change

Find the percent of increase from \displaystyle \small 10 to \displaystyle \small 13.

Possible Answers:

\displaystyle \small 35\%

\displaystyle \small 25\%

\displaystyle \small 90\%

\displaystyle \small 30\%

Correct answer:

\displaystyle \small 30\%

Explanation:

For this type of problem we use this formula: 

\displaystyle \small \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 \small \frac{13-10}{10} \times 100 = \frac{3}{10}\times 100 =30\%.

This our percent increase.

Example Question #24 : Percent Of Change

Find the percent of increase from \displaystyle \small 26 to \displaystyle \small 35

Possible Answers:

\displaystyle \small 45\%

\displaystyle \small \approx35\%

\displaystyle \small \approx32\%

\displaystyle \small \approx95\%

Correct answer:

\displaystyle \small \approx35\%

Explanation:

For this type of problem we use this formula: 

\displaystyle \small \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 \small \small \frac{35-26}{26} \times 100 = \frac{9}{26}\times 100 \approx35\%.

This our percent increase.

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