# Algebra 1 : How to find the percent of decrease

## Example Questions

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### Example Question #1 : How To Find The Percent Of 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 , which is  or .

### Example Question #2 : How To Find The Percent Of Decrease

To encourage more sales, a store has lowered the price of a particular video game from $50 to$40. What is the percentage price decrease?

%

%

%

%

%

%

Explanation:

To find the percent of change, you must divide the difference between the original and new amounts by the original amount. In this case, it would be , or , which is equivalent to 20%.

### Example Question #3 : How To Find The Percent Of Decrease

In a town, the population was 67,000. A disease epidemic strikes this town wiping 9,000 people out. What is the percent decrease of the population.

15.0%

13.2%

8.9%

5.7%

13.4%

13.4%

Explanation:

So the change in population is 9,000. The percentage of population loss is just the change in population divided by the original population.

Turn 0.134 into a percent so that we get 13.4%.  So the percent of population loss is 13.4%.

### Example Question #4 : How To Find The Percent Of Decrease

A farmer began the growing season with 120 acres of wheat. A severe flood recently devastated much of the region, and only 84 acres of wheat remain. By what percentage has the original amount of planted land (120 acres) decreased?

30%

25%

16%

24%

70%

30%

Explanation:

To find the percent decrease, we need to calculate the difference between the original (larger) amount of land and the final (smaller) amount. Here, this difference is  acres. This value refers to the amount of decrease. We now need to convert it into a percent.

To do so, we use a proportion: .

Cross-multiplication shows us that  is equal to

, so percent.

### Example Question #1 : How To Find The Percent Of Decrease

The price of a bike dropped from  to .  Disregard sales tax.  What is the approximate percent decrease?

Explanation:

Write the formula to find percent decrease:

Subsitute the values into the formula.

The approximate percent decrease is .

### Example Question #6 : How To Find The Percent Of Decrease

In 1983 there were an estimated 6,000 snow leopards in the world, but now scientists believe there are only around 3,500. By what percent has the snow leopard population declined since 1983? Round your answer to the nearest tenth of a percent.

Explanation:

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

Now we want to figure out what percent that change was of the original. In other words, 2,500 is what percent of 6,000. We can write that as a solvable equation knowing that "of" means multiply:

divide both sides by 6,000

multiply by 100 to convert this decimal into a percentage

### Example Question #7 : How To Find The Percent Of Decrease

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:

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

### Example Question #8 : How To Find The Percent Of Decrease

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?

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:

.

This means our answer is 10.5%.

### Example Question #9 : How To Find The Percent Of Decrease

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.

Explanation:

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

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:

divide both sides by 501,662

multiply by 100 to convert this decimal into a percentage

### Example Question #10 : How To Find The Percent Of Decrease

What is the percent decrease from  to

Explanation:

To find the percent change of two numbers, you use the formula:

.

This formula in the context of this question:

.

Thus, now know that if we subtract about forty six percent of the original number from the original number, we would get the second number. We have about a forty six percent decrease.

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