Percent of Change - Algebra 1

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Question

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?

Answer

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 .

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Question

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?

Answer

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 $\frac{50-40}{50}$ , or $\frac{10}{50}$ , which is equivalent to 20%.

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Question

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?

Answer

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: $\frac{36}{120} = \frac{x}{100}$ .

Cross-multiplication shows us that is equal to

$\frac{36}{120}\cdot 100$ , so $x=\frac{3}{10}(100)=30$ percent.

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Question

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.

Answer

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

$x=\frac{9,000}{67,000}=0.134$

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

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Question

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

Answer

Write the formula to find percent decrease:

$\textup{Percent Decrease}= \frac{\textup{Old-New}}{\textup{Old}} \times 100%$

Subsitute the values into the formula.

$\frac{75.99-52.99}{75.99} \times 100%= 30.267$

The approximate percent decrease is .

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Question

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

Answer

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.

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Question

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?

Answer

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%.

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Question

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.

Answer

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

$\small 22.2 % = x$

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Question

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.

Answer

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

$\small 6,000 - 3,500 = 2,500$

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:

$\small 2,500 = \frac{x}{100}*6,000$ divide both sides by 6,000

$\small 0.417\approx \frac{x}{100}$ multiply by 100 to convert this decimal into a percentage

$\small 41.7 % = x$

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Question

What is the percent decrease from $\small 312$ to $\small 170$ ?

Answer

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

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

This formula in the context of this question:

$\small \small \frac{312-170}{312}\times100 = \frac{142}{312}\times 100 = \frac{71}{156}\times 100 \approx45.5%$ .

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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Question

What is the percent decrease from to ?

Answer

To find the percent of decrease from one number to the next we use the formula:

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

In this case, the difference is

$\small 38-24 = 14$ .

So our formula would be

$\small \frac{14}{38}\times100 \approx 37%$ .

From $\small 38$ to $\small 24$ is about a $\small 37%$ decrease.

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Question

For your 16th birthday, your parents have decided to help you buy a car. The car you want costs $2500. Your parents said they would contribute $700 toward the purchase price of the car. What was the percent decrease in the price you have to pay for the new car after their contribution?

Answer

To calculate the percent decrease in a price, quantity etc. you need to establish a ratio between the new and lower price and the old, higher price. Then convert to a percentage by multiplying by 100.

Establish a ratio between the new and the old:

$\frac{1800}{2500}=.72$

Convert to a percentage:

percent

So the parental discount amounts to 72% of the old price. In other words with their help, you will only pay 72% of the original price. Because you are now paying only 72% of that price, that was a decrease of 28% (100-72=28%).

Alternatively find the difference between the two prices, divide by the original price, and multiply by 100. Try this method to see that you get the SAME answer.

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Question

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?

Answer

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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Question

Charlie bought stock initially valued at . Unfortunately, Charlie's stocks depreciated to a value of . By what percent did Charlie's stocks depreciate?

Answer

First we want to get the total cash value of depreciation and divide that by the initial stock value:

$\frac{$15000-$10937.43}{$15000}=\frac{$4062.57}{$15000}=0.271$

To get the percent value of decrease, we then multiply the given decimal by :

$0.271\cdot100%=27.1%$

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Question

Jimmy's magazine kiosk has seen a decline in sales for January. December sales totaled , while January's profits were . What is the percent decrease from December to January sales?

Answer

To find the percent of decrease, we take the difference in sales and divide that by the original sales income:

$\frac{$2,300-$1,950}{$2,300}=0.152\ 0.152\cdot100%=15.2%$

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Question

Dr. Beverly Crusher is looking at how many patients she has treated over the last several years. She is interested to see how many patients have had the flu each year. She notices that last year she treated patients and this year she treated patients. She wants to keep track of the percent decrease of patients from last year to this year. Find the percent decrease in patients.

Answer

To find the percent decrease, we need to find how many less patients she has treated (the decrease). This is just taking the difference between the patients she treated last year and those she treated this year,

Now we can just divide this number by the total patients she treated last year to get a decimal,

$\frac{85-73}{85}=\frac{12}{85}=0.141$

To turn it into a percentage you just multiply it by

The formula to get the percent decrease is the decrease divided by the initial total, multiplied by

$\frac{85-73}{85}\times 100 %=14.1 %$

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Question

Paul wanted to sell his car last year. At the time, he was fairly certain that his car was worth $15000. 1 year later, Paul has finally gotten around to selling his car. Unfortunately, due to depreciation in value, the car is only worth $12000. By what percent, did Paul’s car decrease in value?

Answer

Let represent the original value of Paul's car (its value 1 year ago) and represent the new value of Paul's car (its value today). Using these variables, we can calculate the percent decrease in the car's value with the following expression:

$\left(\frac{N-O}{O}\right)100$

Plug in the appropriate values into this expression.

$\left(\frac{12000-15000}{15000}\right)100$

Paul's car lost 20% of its value in 1 year.

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Question

The cost of milk last week was $2.50 a gallon. This week, it is on sale for $2 a gallon. Find the percent of decrease.

Answer

To find the percent of decrease, we use the formula

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

So, we will substitute our values.

We get

$\text{percent decrease} = \frac{2.50 - 2.00}{2.50} \cdot 100$

$\text{percent decrease} = \frac{0.50}{2.50} \cdot 100$

$\text{percent decrease} = 0.20 \cdot 100$

$\text{percent decrease} = 20%$

Therefore, the percent decrease is 20%.

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Question

Last week, the price of carrots at the farmer's market was a pound. This week, it is a pound. Find the percent decrease rounded to the nearest percent.

Answer

To find percent decrease, we use the following formula:

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

So, if we substitute, we get

$\text{percent decrease} = \frac{$1.50 - $1.00}{$1.50} \cdot 100$

$\text{percent decrease} = \frac{$0.50}{$1.50} \cdot 100$

$\text{percent decrease} = 0.33333 \cdot 100$

$\text{percent decrease} = 33.333%$

If we round to the nearest percent, we get 33%.

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Question

You decide that 15 pairs of shoes is far too many and sell 8 of them. Your percent decrease in shoes is?

Answer

Subtract the new value from the old value:

Divide by the original number:

$7\div15=.4666666667$

Multiply by 100:

A 47% decrease in shoes.

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