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Algebra 1 : Percents

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Example Questions

Example Question #1 : Percents

45 is what percent of 75?

Possible Answers:

$45\%$

$60\%$

$167\%$

$67\%$

$6\%$

Correct answer:

$60\%$

Explanation:

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

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

Divide both sides by 75.

$x= \frac{45}{75}=0.6$

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

x * 100 = 0.6*100=60 %

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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:

33.33%

0.36%

35.53%

35.52%

0.33%

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%.

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Example Question #2 : Percents

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

Possible Answers:

$\frac{2,000}{N}$ %

$\frac{20}{N}$ %

$\frac{50}{N}$ %

$\frac{5,000}{N}$ %

Correct answer:

$\frac{2,000}{N}$ %

Explanation:

Set up a proportion statement.

$\frac{P}{100} = \frac{20}{N}$

Solve for :

$\frac{P}{100} \cdot 100 = \frac{20}{N}\cdot 100$

$P = \frac{2,000}{N}$

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Example Question #3 : Percents

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

Possible Answers:

$\frac{5N}{2}$ %

$\frac{2N}{5}$ %

$\frac{N}{4}$ %

$\frac{5N}{4}$ %

Correct answer:

Explanation:

Set up a proportion statement.

$\frac{P}{100} = \frac{N}{25}$

Solve for :

$\frac{P}{100} \cdot 100 = \frac{N}{25}\cdot 100$

P = 4N

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Example Question #1 : Percents

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

Possible Answers:

$\frac{50}{N}$ %

$\frac{5,000}{N}$ %

$\frac{20}{N}$ %

$\frac{2,000}{N}$ %

Correct answer:

$\frac{5,000}{N}$ %

Explanation:

Set up a proportion statement.

$\frac{P}{100} = \frac{50}{N}$

Solve for :

$\frac{P}{100} \cdot 100 = \frac{50}{N}\cdot 100$

$P = \frac{5,000}{N}$

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Example Question #5 : Percents

Convert $1025\%$ into a improper fraction.

Possible Answers:

$\frac{25}{2}$

$\frac{11}{4}$

$\frac{5}{2}$

$\frac{41}{4}$

$\frac{41}{40}$

Correct answer:

$\frac{41}{4}$

Explanation:

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

$\frac{1025}{100}= 10.25$

The decimal 0.25 can be converted to a fraction by moving the decimal place two places to the right and dividing by 100.

$0.25= \frac{25}{100} = \frac{1}{4}$

$10+\frac{1}{4}= 10\frac{1}{4}= \frac{41}{4}$

The correct answer is: $\frac{41}{4}$

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Example Question #7 : Percents

If $\small 35\%$ of the freshman got an A on their French exam, $\small 25\%$ got a B, $\small 19\%$ got a C. What percentage of freshman got a D or below?

Possible Answers:

$\small 39\%$

$\small 79\%$

$\small 11\%$

$\small 21\%$

Correct answer:

$\small 21\%$

Explanation:

To answer this problem, we must know that a whole is equal to $\small 100\%$ . With this knowledge, we understand that the percentages must add up to one hundred. The percentages provided add up to

$\small 79\%; 35+25+19 = 79.$

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:

$\small 79 + x = 100$ .

To solve for x, we simply subtract $\small 79$ from both sides, leaving us with $\small x = 21\%.$

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Example Question #1 : Percents

What percent of is ?

Possible Answers:

$9\%$

$\frac{1}{9}\%$

$900\%$

$90\%$

$9000\%$

Correct answer:

$900\%$

Explanation:

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

$\left(\frac{x}{100\%}\right)(6)=54$

Solve for .

First divide by 6 on both sides.

$\left(\frac{x}{100}\%\right)=9$

Next multiply by 100 on both sides.

$x=900\%$

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Example Question #1 : 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:

$\$32.96$

$\$37.17$

$12.39

$\$14.87$

$\$12.39$

Correct answer:

$\$37.17$

Explanation:

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

(49.56)(1-0.25)

(49.56)(0.75)

$\$37.17$

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Example Question #10 : Percents

The Aral Sea located in Asia Minor originally had a surface area of $68,000\:km^{2}$ 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 $17,200\: km^{2}$ . What percent of the total lake surface area has been lost due to human incompitance?

Possible Answers:

$25\%$

$50\%$

$90\%$

$75\%$

$67\%$

Correct answer:

$75\%$

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:

$68,000 \,km^{2}-17,200\,km^{2}=50,800\,km^{2}$

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

$\frac{50,800\, km^{2}}{68,000\, km^{2}}=0.747$

This decimal multiplied by 100 will provide us with our percentage:

$0.747 \cdot100\%= 74.7\%$

This value can be rounded up to $75\%$

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Algebra 1 : Percents

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Percents

Example Question #1 : Percents

Example Question #2 : Percents

Example Question #3 : Percents

Example Question #1 : Percents

Example Question #5 : Percents

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