Algebra 1 : Percents

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1087 : Linear Equations

45 is what percent of 75?

Possible Answers:

Correct answer:

Explanation:

Let equal the decimal value of our answer. We can set up the following equation.

 (i.e. 75 times what percent equals 45?)

Divide both sides by 75.

Multiply by 100 to get the percentage value of the decimal.

%

Example Question #1 : Percents

In a bag of marbles, Barry has 20 green ones and 40 red ones.  If he adds 7 green and 9 red, what percentage (to the nearest hundreth) of the marbles will be green?

Possible Answers:

35.52%

33.33%

35.53%

0.33%

0.36%

Correct answer:

35.53%

Explanation:

First, you need to add in the marbles.  This will give you 27 green and 49 red.  The total number of marbles in the bag are 76.  To find the percentage of green marbles, all you need to do is divide 27 by 76, which gives you 0.35526315789474 or 35.526315789474%.  Rounding to the nearest percent, you get 35.53%.

Example Question #1 : Percents

Let  be a positive real number. In terms of , what percent of  is 20?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Set up a proportion statement.

Solve for :

Example Question #2 : Percents

Let  be a positive real number. In terms of , what percent of 25 is ?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Set up a proportion statement.

Solve for :

Example Question #3 : Percents

Let  be a positive real number. In terms of , what percent of  is 50?

Possible Answers:

 %

 %

 %

 %

 %

Correct answer:

 %

Explanation:

Set up a proportion statement.

Solve for :

Example Question #5 : Percents

Convert  into a improper fraction.

Possible Answers:

Correct answer:

Explanation:

Eliminate the percentage sign and divide by 100.  This will give the true value of the number without the percent sign.

The decimal  can be converted to a fraction by moving the decimal place two places to the right and dividing by 100.

The correct answer is: 

Example Question #6 : Percents

If  of the freshman got an A on their French exam,  got a B,  got a C. What percentage of freshman got a D or below? 

Possible Answers:

Correct answer:

Explanation:

To answer this problem, we must know that a whole is equal to . With this knowledge, we understand that the percentages must add up to one hundred. The percentages provided add up to 

 

Since we are looking for an amount that is besides what is given, we will call that unknown "x", thus based on the idea that we must add up all percentages to one hundred to make a whole, our equation will look like this: 

.

To solve for x, we simply subtract  from both sides, leaving us with 

Example Question #7 : Percents

What percent of  is ?

Possible Answers:

Correct answer:

Explanation:

Write the equation to express this scenario.  The percentage of a number is divided by 100 percent.

Solve for .

First divide by 6 on both sides.

Next multiply by 100 on both sides.

Example Question #7 : Percents

The original price of a pair of shoes is $49.56. There is a special sale going on that is 25% off all shoes. How much do the shoes cost during the sale?

Possible Answers:

Correct answer:

Explanation:

Taking 25% off a price means we are paying for 75% of the original cost.

Example Question #8 : Percents

The Aral Sea located in Asia Minor originally had a surface area of   and was one of the largest lakes in the world. Due to irresponsible water use, the lake has shrunk and now has a surface area of . What percent of the total lake surface area has been lost due to human incompitance? 

Possible Answers:

Correct answer:

Explanation:

First of all, since we are looking for the percent of surface area lost (not the surface area remaining), we subtract the remaining surface area from the initial to determine the lost area:

Dividing the lost surface area over the original surface area provides us with a decimal ratio of the water surface area lost:

This decimal multiplied by  will provide us with our percentage:

This value can be rounded up to 

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