Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #90 : Percent Of Change

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

Possible Answers:

\(\displaystyle 45\%\)

\(\displaystyle 48\%\)

\(\displaystyle 24\%\)

\(\displaystyle 52\%\)

Correct answer:

\(\displaystyle 48\%\)

Explanation:

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

 

To find the percent of decrease, we need to divide the difference by the original number:

\(\displaystyle 150,000-78,560=71440\)

\(\displaystyle \frac{71440}{150000}=.476\approx48\%\)

So the number of Republican voters decreased by about \(\displaystyle 48\%\)

Example Question #90 : Percent Of Change

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

Possible Answers:

\(\displaystyle 45\%\)

\(\displaystyle 48\%\)

\(\displaystyle 24\%\)

\(\displaystyle 52\%\)

Correct answer:

\(\displaystyle 48\%\)

Explanation:

If the number of Republican voters in a certain district has decreased from 150,000 to 78,560, what is the percent decrease in the number of Republican voters?

 

To find the percent of decrease, we need to divide the difference by the original number:

\(\displaystyle 150,000-78,560=71440\)

\(\displaystyle \frac{71440}{150000}=.476\approx48\%\)

So the number of Republican voters decreased by about \(\displaystyle 48\%\)

Example Question #2881 : Algebra 1

At a clothing store, a dress costs $79.99. After the dress was worn at a red carpet movie premiere, the clothing store decides to up the price of the dress to $119.99. What is the percent change in the price of the dress?

Possible Answers:

\(\displaystyle 35\%\)

\(\displaystyle 40\%\)

\(\displaystyle 50\%\)

\(\displaystyle 75\%\)

\(\displaystyle 65\%\)

Correct answer:

\(\displaystyle 50\%\)

Explanation:

The percent change formula is new amount minus old amount then divided by old amount and multiplied by 100. In this case the formula should be

\(\displaystyle \frac{119.99-79.99}{79.99}\cdot100\)

\(\displaystyle \frac{40}{79.99}\cdot100\)

\(\displaystyle 0.50\cdot100\)

\(\displaystyle 50\%\)

The price of the dress increased by 50%

Example Question #92 : Percent Of Change

Megan enrolled in a college biology course and received test grades of 63%, 80%, 42%, and 51%. Since she failed the course, she needed to retake it. This time, she received test grades of 80%, 91%, 84%, and 80%. What was the percentage change in her average test score from the first time she took the class to the second time? (Round your answer to the nearest whole percent)

Possible Answers:

\(\displaystyle 40\%\)

\(\displaystyle 34\%\)

\(\displaystyle 29\%\)

\(\displaystyle 25\%\)

\(\displaystyle 42\%\)

Correct answer:

\(\displaystyle 42\%\)

Explanation:

The first step is finding the average test scores Megan received for each time she took the course. To find an average, add up all the scores and divide by the amount of scores.

For the first time she took the class the average is

\(\displaystyle \frac{63+80+42+51}{4}\)

\(\displaystyle \frac{236}{4}\)

\(\displaystyle 59\%\)

For the second time she took the class the average is

\(\displaystyle \frac{80+91+84+80}{4}\)

\(\displaystyle \frac{335}{4}\)

\(\displaystyle 83.75\%\)

Now, it is very important to understand that while her grade improved from 59% to 83.75% the difference between those two (24.75%) is not the percent change from her first score to the second. You still need to use the percent change formula of new amount subtracted by the old amount then divided by the old amount and multiplied by 100.

\(\displaystyle \frac{83.75-59}{59}\cdot100\)

\(\displaystyle \frac{24.75}{59}\cdot100\)

\(\displaystyle 0.4195\cdot100\)

\(\displaystyle 41.95\%\)

Rounded to the nearest whole percent this is \(\displaystyle 42\%\). Megan's score change from 59 to 83.75 is a 42% increase.

Example Question #92 : How To Find The Percent Of Increase

At your job, you are currently making $10 an hour.  Your boss says you are doing a great job and wants to give you a raise.  You now make $12 an hour.  Find the percent increase.

Possible Answers:

\(\displaystyle 15\%\)

\(\displaystyle 2\%\)

\(\displaystyle 1\%\)

\(\displaystyle 20\%\)

\(\displaystyle 12\%\)

Correct answer:

\(\displaystyle 20\%\)

Explanation:

To find the percent increase, we use the formula

\(\displaystyle \text{percent increase} = \frac{\text{new price} - \text{old price}}{\text{old price}} \cdot 100\)

We know

\(\displaystyle \text{new price} = \$12\)

\(\displaystyle \text{old price} = \$10\)

so we can substitute into the equation.  We get

\(\displaystyle \text{percent increase} = \frac{\$12-\$10}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$2}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{1}{5} \cdot 100\)

\(\displaystyle \text{percent increase} = 20\)

Therefore, the percent increase is 20%.

Example Question #91 : How To Find The Percent Of Increase

A number five is increased to twelve.  What is the percent increase?

Possible Answers:

\(\displaystyle 140\%\)

\(\displaystyle 14\%\)

\(\displaystyle 220\%\)

\(\displaystyle 70\%\)

\(\displaystyle 120\%\)

Correct answer:

\(\displaystyle 140\%\)

Explanation:

Write the percentage increase or decrease formula.

\(\displaystyle \%\textup{ increase or decrease}= \frac{\textup{New-Original}}{\textup{Original}} \times 100\%\)

If our final answer is a positive percentage, we will have a percent increase.  Otherwise, a negative answer will indicate a percent decrease.

The original number is 5.  The new number is 12.  Substitute the numbers.

\(\displaystyle \frac{12-5}{5} \times 100\%\)

Simplify this expression.

\(\displaystyle \frac{7}{5} \times 100\% = 1\frac{2}{5} \times 100\%= 1.4\times 100\% = 140 \%\)

This transition is a \(\displaystyle 140\%\) increase.

Example Question #94 : How To Find The Percent Of Increase

Last month you got paid $10 an hour at your job.  You went under review this month, and they said they are increasing your pay to $12 an hour.  Find the percent increase.

Possible Answers:

\(\displaystyle 20\%\)

\(\displaystyle 10\%\)

\(\displaystyle 2\%\)

\(\displaystyle 25\%\)

\(\displaystyle 15\%\)

Correct answer:

\(\displaystyle 20\%\)

Explanation:

To find percent increase, we use the formula

\(\displaystyle \text{percent increase} = \frac{\text{new amount - original amount}}{\text{original amount}} \cdot 100\)

We can substitute into the formula.  We get

\(\displaystyle \text{percent increase} = \frac{\$12 - \$10}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$2}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = 20\)

Therefore, the percent increase is equal to 20%.

 

 

Example Question #95 : How To Find The Percent Of Increase

The temperature on two consecutive days was \(\displaystyle 80\) and \(\displaystyle 90\) degrees F. What is the percent increase of the temperature from the first to second day?

Possible Answers:

\(\displaystyle 112.5\)

\(\displaystyle 11.11\)

\(\displaystyle 88.89\)

\(\displaystyle 12.5\)

Correct answer:

\(\displaystyle 12.5\)

Explanation:

To find the percent increase, we must find the amount that increased, divided by the original amount:

\(\displaystyle \frac{90-80}{80}=\frac{1}{8}\)

As a percent, we take this fraction and multiply by 100:

\(\displaystyle \frac{100}{8}=12.5\)

 

Example Question #96 : How To Find The Percent Of Increase

Last week, a gallon of milk cost $3.00.  This week, the cost of a gallon of milk is $3.75.  Find the percent increase.

Possible Answers:

\(\displaystyle 75\%\)

\(\displaystyle 25\%\)

\(\displaystyle 12.5\%\)

\(\displaystyle 60\%\)

\(\displaystyle 50\%\)

Correct answer:

\(\displaystyle 25\%\)

Explanation:

To find the percent increase, we use the following formula:

\(\displaystyle \text{percent increase} = \frac{\text{new price - original price}}{\text{original price}} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$3.75 - \$3.00}{\$3.00} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$0.75}{\$3.00} \cdot 100\)

\(\displaystyle \text{percent increase} = 0.25 \cdot 100\)

\(\displaystyle \text{percent increase} = 25\%\)

 

Example Question #97 : How To Find The Percent Of Increase

Last month at your job, you were paid $10 an hour.  This month, you received a raise and now earn $13 an hour.  Find the percent increase.

Possible Answers:

\(\displaystyle 30\%\)

\(\displaystyle 3\%\)

\(\displaystyle 25\%\)

\(\displaystyle 12.5\%\)

\(\displaystyle 17\%\)

Correct answer:

\(\displaystyle 30\%\)

Explanation:

To find the percent increase, we will use the following formula:

\(\displaystyle \text{percent increase} = \frac{\text{new price - original price}}{\text{original price}} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$13 - \$10}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = \frac{\$3}{\$10} \cdot 100\)

\(\displaystyle \text{percent increase} = 0.30 \cdot 100\)

\(\displaystyle \text{percent increase} = 30\%\)

 

Therefore, the percent increase of your pay from last month to this month is 30%.

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