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Algebra 1 : Algebra 1

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Example Questions

Example Question #11 : How To Find The Percent Of Decrease

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?

Possible Answers:

$28\%$

$27\%$

$72\%$

$\textup{None of the other answers}$

$82\%$

Correct answer:

$28\%$

Explanation:

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:

.72*100=72 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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Example Question #13 : How To Find The Percent Of Decrease

Jimmy's magazine kiosk has seen a decline in sales for January. December sales totaled $\$2,300$ , while January's profits were $\$1,950$ . What is the percent decrease from December to January sales?

Possible Answers:

$14.7\%$

$12.5\%$

$17.9\%$

$15.2\%$

$18\%$

Correct answer:

$15.2\%$

Explanation:

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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Example Question #14 : How To Find The Percent Of Decrease

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?

Possible Answers:

$75\%$

$83.3\%$

$9.7\%$

$80.3\%$

$90.3\%$

Correct answer:

$90.3\%$

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 $100\%$ , giving us a percent value:

$0.903\cdot100\%=90.3\%$

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Example Question #15 : How To Find The Percent Of Decrease

Charlie bought stock initially valued at $\$15000$ . Unfortunately, Charlie's stocks depreciated to a value of $\$10937.43$ . By what percent did Charlie's stocks depreciate?

Possible Answers:

$37.1\%$

$72.9\%$

$27.1\%$

$25\%$

$33.3\%$

Correct answer:

$27.1\%$

Explanation:

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 $100\%$ :

$0.271\cdot100\%=27.1\%$

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Example Question #121 : Percent Of Change

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?

Possible Answers:

$40\%$

$20\%$

$50\%$

$30\%$

$25\%$

Correct answer:

$20\%$

Explanation:

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.

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

$-20\%$

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

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Example Question #11 : How To Find The Percent Of Decrease

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.

Possible Answers:

$20\%$

$5\%$

$25\%$

$12\%$

$10\%$

Correct answer:

$20\%$

Explanation:

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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Example Question #18 : How To Find The Percent Of Decrease

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 73{} patients. She wants to keep track of the percent decrease of patients from last year to this year. Find the percent decrease in patients.

Possible Answers:

$12 \%$

$14.1 \%$

$45.7 \%$

$6.3 \%$

Correct answer:

$14.1 \%$

Explanation:

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,

85-73=12

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 $100 \%$

The formula to get the percent decrease is the decrease divided by the initial total, multiplied by $100 \%$

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

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Example Question #19 : How To Find The Percent Of Decrease

Last week, the price of carrots at the farmer's market was $\$ 1.50$ a pound. This week, it is $\$ 1.00$ a pound. Find the percent decrease rounded to the nearest percent.

Possible Answers:

$50\%$

$-50\%$

$33\%$

$25\%$

$12\%$

Correct answer:

$33\%$

Explanation:

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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Example Question #11 : How To Find The Percent Of Decrease

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

Possible Answers:

$20\%$

$52\%$

None of the other answers.

$27\%$

$35\%$

Correct answer:

$27\%$

Explanation:

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

200-146=54

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

$.27*100=27\%$

A 27% decrease.

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Example Question #2911 : Algebra 1

Kerri wanted to make a chart to calculate how much time she was spending on studying for her tests. For her midterm, she charted that she spent 1 hour and 30 minutes studying every day for three days. Since she was grasping the material, for the final exam Kerri only studied 3 hours total. What is the percent change for the amount of time studying between the midterm and final exam?

Possible Answers:

$-28.1\%$

$-51.2\%$

$-37.7\%$

$-27.8\%$

$-33.3\%$

Correct answer:

$-33.3\%$

Explanation:

The first task to do in this problem is to convert the time amounts for studying to either minutes or hours. The problem says Kerri spent three days of studying for 1 hour and 30 minutes each, which is also 1.5 (30 minutes is half an hour) hours. Multiply 3 days by 1.5 hours o get 4.5 hours of total studying for her midterm. Since the final exam is already in the unit of hours the amount of 3 hours is ready to be worked with.

Use the percent change formula new amount subtracted by old amount then divided by the old amount and multiplied by 100 to find the percent change.

$\frac{3-4.5}{4.5}\cdot 100$

$\frac{-1.5}{4.5}\cdot 100$

$-0.333\cdot 100$

$-33.3\%$

Kerri studied 33.33% less for the final exam than she did for the midterm.

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : How To Find The Percent Of Decrease

Example Question #13 : How To Find The Percent Of Decrease

Example Question #14 : How To Find The Percent Of Decrease

Example Question #15 : How To Find The Percent Of Decrease

Example Question #121 : Percent Of Change

Example Question #11 : How To Find The Percent Of Decrease

Example Question #18 : How To Find The Percent Of Decrease

Example Question #19 : How To Find The Percent Of Decrease

Example Question #11 : How To Find The Percent Of Decrease

Example Question #2911 : Algebra 1

All Algebra 1 Resources

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