Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : Percents

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

Possible Answers:

 %

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 %

 %

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 #7 : 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 #1 : 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 #2 : 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 #10 : 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 

Example Question #11 : Percents

What is ten percent of six?

Possible Answers:

Correct answer:

Explanation:

In order to determine the value, set up an expression.

Ten percent is ten parts out of 100, or .

Ten percent of six would be:

Simplify this to find the unknown value.

The answer is:  

Example Question #12 : Percents

Convert  to decimal.

Possible Answers:

Correct answer:

Explanation:

To convert a percent to a decimal, simply remove the percent sign and divide the entire number by 100.

This is also the same as moving the decimal place back two spaces.

The answer is:  

Example Question #11 : Percents

Convert the following decimal to percent:  

Possible Answers:

Correct answer:

Explanation:

A percentage is a number out of 100, which means that if we have a number that was 54 percent, then we have: 

From this example, since we are given a decimal , we can work backwards to find the percentage by moving the decimal place two spots to the right and add a percentage sign.

The answer is:  

Example Question #1091 : Algebra 1

 is what percent of ?

Possible Answers:

Correct answer:

Explanation:

Seeing the word means equal and of is multiplication. We set up an equation. 

 Let  represent the percentage. Divide  on both sides.

 We shift the decimal two places to the left to find the percentage.

%

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