Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #11 : How To Find The Part From The Whole With Percentage

What is \displaystyle 60\% of \displaystyle 300?

Possible Answers:

\displaystyle 200

\displaystyle 150

\displaystyle 130

\displaystyle 60

\displaystyle 180

Correct answer:

\displaystyle 180

Explanation:

To find 60 percent of something, we first need to convert 60 percent into a decimal. We do this by dividing 60 percent by one hundred.

This results in the decimal,

\displaystyle \frac{60\%}{100}=0.60

Now we will mutiply 300 by 0.60.

\displaystyle 300\cdot (0.60)=180

Example Question #13 : How To Find The Part From The Whole With Percentage

Granada High School has a graduating class of \displaystyle 700 seniors. If \displaystyle \small 20\% of the high school graduates scored above an \displaystyle \small 80\% on their final exam, and \displaystyle \small 59\% of the graduated scored above a \displaystyle \small 60\%, how many students scored \displaystyle \small 59\% or less on their final? 

Possible Answers:

\displaystyle \small 47\%

\displaystyle \small 147

\displaystyle 23.4

\displaystyle \small 21\%

\displaystyle \small 209

Correct answer:

\displaystyle \small 147

Explanation:

Granada High School has a graduating class of 700 seniors. If \displaystyle \small 20\% of the high school graduates scored above an \displaystyle \small 80\% on their final exam, and \displaystyle \small 59\% of the graduated scored above a \displaystyle \small 60\%, how many students scored \displaystyle \small 59\% or less on their final? 

First, we must find the percentage of seniors that scored below a \displaystyle \small 59\%. To do this we subtract the \displaystyle \small 20\% and \displaystyle \small 59\% of students who scored \displaystyle \small 60\% and above from \displaystyle \small 100\%. This leaves us with a remaining \displaystyle \small 21\% of graduates who did not score above a \displaystyle \small 59\%. Next, we find out exactly how many students equal \displaystyle \small 21\% of the graduating class. To do this we multiply the percentage in decimal form, \displaystyle 0\small .21, against the total number of students, \displaystyle \small 700.

So \displaystyle 0\small \small .21\times700 =147.

So, \displaystyle \small 147 of the graduating class did not score above a \displaystyle \small 60\%.

Example Question #3201 : Algebra 1

What is \displaystyle 3\% of \displaystyle 150?

Possible Answers:

\displaystyle 45

\displaystyle \small 4.5

\displaystyle \small 500

\displaystyle \small 50

\displaystyle \small 5,000

Correct answer:

\displaystyle \small 4.5

Explanation:

To find 3% of anything, convert it into a decimal. 3% as a decimal is 0.03.

Then we can multiply 150 by 0.03 to get an answer of 4.5.

We could also get this in another way.

3% is just \displaystyle \small \frac{3}{100}.

150 is \displaystyle \small 100+\small \frac{1}{2}(100), and \displaystyle \small 3 + \frac{1}{2}(3) = 4.5.

Example Question #3201 : Algebra 1

What is \displaystyle 15\% of \displaystyle 327?

Possible Answers:

\displaystyle \small 21.8

\displaystyle \small 49.05

\displaystyle \small 218

\displaystyle \small 2,180

\displaystyle \small 490.5

Correct answer:

\displaystyle \small 49.05

Explanation:

To find 15% of anything, just multiply by 0.15, its decimal equivalent.

In this case, 327 times 0.15 is 49.05.

\displaystyle 327\cdot 0.15=49.05

Example Question #12 : How To Find The Part From The Whole With Percentage

What is \displaystyle 46\% of \displaystyle 218 ?

Possible Answers:

\displaystyle 100.28

\displaystyle 172

\displaystyle 108.98

\displaystyle 10.028

\displaystyle 92

Correct answer:

\displaystyle 100.28

Explanation:

To find the part from the whole given a percentage, we multiply the whole by the decimal equivalent of the percentage. To find this, we divide the percentage by one-hundred:

\displaystyle 46\% \div 100 = .46

\displaystyle .46 \times 218 = 100.28

Therefore, \displaystyle 46\% of \displaystyle 218 is \displaystyle 100.28

Example Question #17 : How To Find The Part From The Whole With Percentage

As of the middle of August, Magnus had saved \displaystyle 74\% of his total travel budget. If Magnus has a goal of saving \displaystyle \$6,500 , how much does he have left to save?

Possible Answers:

\displaystyle \$4810

\displaystyle \$74

\displaystyle \$740

\displaystyle \$1690

Correct answer:

\displaystyle \$1690

Explanation:

As of the middle of August, Magnus had saved \displaystyle 74\% of his total travel budget. If Magnus has a goal of saving \displaystyle \$6,500 , how much does he have left to save?

There are two ways to go about doing this, and both of them require you to look for what is actually being asked. The question asks you for how much he has left to save. This means that we are not looking for \displaystyle 74\%, we are looking for \displaystyle 26\% of the savings goal. So, the simpler way to solve this is to do the following:

\displaystyle \$6500\cdot .26=\$1690

Note, we also could have found \displaystyle 74\% of \displaystyle \$6,500 and then subtracted that from \displaystyle \$6,500. Using this method would have yielded the exact same answer as the other method. 

Example Question #12 : How To Find The Part From The Whole With Percentage

The human body is roughly \displaystyle 80\% water. If Oscar weighs \displaystyle 170\,lbs, what is his dry weight (weight without water)?

Possible Answers:

\displaystyle 42\,lbs

\displaystyle 36\,lbs

\displaystyle 136\,lbs

\displaystyle 26\,lbs

\displaystyle 34\,lbs

Correct answer:

\displaystyle 34\,lbs

Explanation:

Since \displaystyle 80\% of the human body is water and we are looking for the dry weight, we want to find \displaystyle 20\% of \displaystyle 170\,lbs:

\displaystyle \frac{20\%}{100\%}\cdot170\,lbs=34\,lbs

Example Question #13 : How To Find The Part From The Whole With Percentage

Oscar calculated that 35% of the miles he drives in his car are for recreation and the remaining 65% are miles from commuting back and forth from work. If Oscar drives 4002 miles in a given week, how many miles will he have driven commuting to work and back? 

Possible Answers:

\displaystyle 265\,miles

\displaystyle 260\,miles

\displaystyle 140\,miles

\displaystyle 225\, miles

\displaystyle 320\,miles

Correct answer:

\displaystyle 260\,miles

Explanation:

If \displaystyle 65\% of the miles Oscar drives being commuter miles, we can determine how many miles that is by multiplying the total number of miles driven by \displaystyle 65\%:

\displaystyle 0.65\cdot400\, miles=260\,miles

Example Question #20 : How To Find The Part From The Whole With Percentage

44 is what percent of 80?

Possible Answers:

\displaystyle 50\%

\displaystyle 45\%

\displaystyle 55\%

\displaystyle 60\%

\displaystyle 44\%

Correct answer:

\displaystyle 55\%

Explanation:

We know that 80 multiplied by some percentage, equals 44. Because a percent is number, divided by 100, we can represent this problem mathematically, as follows:

\displaystyle 80\left(\frac{x}{100}\right)=44 

To get \displaystyle x by itself, multiply both sides of the equation by 80. This gives us:

\displaystyle \frac{x}{100}=\frac{44}{80}

Then, multiply both sides of the equation by 100. This gives us:

\displaystyle x=(100)(\frac{44}{80})

Simplify.

\displaystyle x=55

Thus, 44 is 55% of 80.

Example Question #41 : Whole And Part

According to a recent poll, \displaystyle 34\% of voters plan on voting for a certain canditate for president. If there are 175 million voters total, how many will vote for this candiate?

Possible Answers:

\displaystyle 5,950,000,000

\displaystyle 595,000,000

\displaystyle 59,500,000

\displaystyle 595,000

Correct answer:

\displaystyle 59,500,000

Explanation:

According to a recent poll, \displaystyle 34\% of voters plan on voting for this candiate for president. If there are 175 million voters total, how many will vote for this candiate?

So out of a total of 175 million, (175,000,000), 34% will vote for this candiate. To find that number, change your percent to a decimal and multiply:

\displaystyle 175,000,000\cdot.34=59,500,000

So a total of \displaystyle 59,500,000 people will vote for this presidential candiate.

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