Percent of Change

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Algebra › Percent of Change

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Find the percent of increase from $\small 15$ to $\small 24$ .

$\small 60%$

$\small 40%$

$\small 90%$

$\small 15%$

Explanation

For this type of problem we use this formula:

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

"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 $\small #$ ____ to ____.

In this problem our formula will be filled in as follows:

$\small \small \frac{24-15}{15} \times 100 = \frac{9}{15}\times 100 = 60%$ .

This is our percent increase.

Find the percent of increase from $\small 15$ to $\small 24$ .

$\small 60%$

$\small 40%$

$\small 90%$

$\small 15%$

Explanation

For this type of problem we use this formula:

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

"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 $\small #$ ____ to ____.

In this problem our formula will be filled in as follows:

$\small \small \frac{24-15}{15} \times 100 = \frac{9}{15}\times 100 = 60%$ .

This is our percent increase.

There are 3000 people enrolled in a specific program in 2003. Between 2003 and 2004, the number of people enrolled increases by 12%, and between 2004 and 2005, 65 people unenroll. How many people are enrolled at the beginning of 2005?

Explanation

Between 2003 and 2004, the number of people enrolled increases by 12%:

$3000\cdot 1.12=3360$

Between 2004 and 2005, 65 people unenroll:

A book was originally priced at $12. It was put on sale for $8. To the nearest percent, by what percentage was its price marked down?

Explanation

This problem is a simple percent chage problem. The absoluge change in price was . Relative to the original price, it was $\frac{4}{12}$ , which is or .

A bag of candy has 200 pieces when opened. After eating some, there are 146 left. What is the percent decrease?

None of the other answers.

Explanation

Find the amount of decrease, divide it by the starting number, and multiply by 100 to convert to a percentage.

$\frac{54}{200}=.27$

A 27% decrease.

A book was originally priced at $12. It was put on sale for $8. To the nearest percent, by what percentage was its price marked down?

Explanation

This problem is a simple percent chage problem. The absoluge change in price was . Relative to the original price, it was $\frac{4}{12}$ , which is or .

In 2013, the population of a city was 390,113 people. The same city had a population of 501,662 people in 1999. By what percent did the population of the city decrease during that time period? Round to the nearest tenth of a percent.

$\small 22.2 %$

$\small 2.22 %$

$\small 77.8 %$

$\small 28.6 %$

$\small 11.1 %$

Explanation

To figure out the percent change, we want to figure out the amount that the population changed. We can do this by subtracting:

$\small 501,662 - 390,113 = 111,549$

Now we want to figure out what percent that change was of the original. In other words, 111,549 is what percent of 501,662. We can write that as a solvable equation knowing that "of" means multiply:

$\small 111,549 = \frac{x}{100}*501,662$ divide both sides by 501,662

$\small 0.222 \approx \frac{x}{100}$ multiply by 100 to convert this decimal into a percentage

$\small 22.2 % = x$

Between January 2nd and February 15th, the number of Christmas trees in windows on Macalaster Lane decreased by . If of the houses originally displayed trees, what percentage of houses still have trees on February 15th?

$\small 10.5 %$

$\small 59.5 %$

$\small 0.105 %$

$\small 0.595 %$

$\small 25.5 %$

Explanation

If the amount of houses decreased by 85%, that means the amount that remain is 100% - 85%, or 15%. We want to find 15% of 70%. Since we're leaving our answer as a percentage, we can just leave 70% as 70, and convert 15% to 0.15 and multiply:

$\small 70*0.15= 10.5$ .

This means our answer is 10.5%.

A pair of shorts at the mall was marked down in price from to . What was the sale percentage on those shorts?

Explanation

To find the percentage that the original price decreased, use the following relation:

$\frac{original-new}{original}=\frac{25-15}{25}=.4$

Now, to find the percentage, simply multiply the decimal by 100.

Oscar brought 72 cookies to a company picnic. By picnic's end there were only 7 cookies left. By what percentage did Oscar's batch of cookies decrease?

Explanation

To determine the percent of decrease, we must first find the difference between the initial and diminished counts and divide the difference by the initial value:

$\frac{72-7}{72}=\frac{65}{72}=0.903$

Next, we multiply the given value by , giving us a percent value:

$0.903\cdot100%=90.3%$

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