The student council decided to conduct a survey to see how many middle school students attend football games on Friday nights. They asked the students when they entered the stadium what grade they were in and then recorded the results. The student council members did this for three weeks to get a good estimate on how many middle school students attend the games. They found that 42% of the 850 students who attended were from the middle school. How many students does this represent?
Proportions can be used to compare any equal quantity. Remember that proportions are created when two ratios are equal. Because of this, proportions can be used to find any missing piece. If you know a percent, you can also find a part of the whole.
Let’s look at an example.
At Big Town Middle School, approximately 37% of the students participate in athletic programs. If there are 968 students at the school, how many uniforms do they need to purchase?
Although 37% is a useful number, it does not tell you how many students need uniforms. You know that for every 100 students, 37 will need a uniform. But that is still not enough information to make a purchase.
Then, divide by 100 to find the number of uniforms to purchase.
The answer is 358.16.
Therefore, the team needs to purchase 358 uniforms.
Since you can use a proportion to solve for any missing variable, you can also find the whole if you know a percent and its corresponding part.
Let’s look at another example.
At Big Town High School, approximately 58% participate in athletic programs. If 1670 students are involved in an athletics program, then how many students are there in the school?
Then, divide by 58 to find the number of students in the school.
The answer is 2879.3.
Therefore there are 2879 students in the school.
Earlier, you were given a problem about the student football crowd.
First, you know that 42% of the students at the games are in middle school. Write the percent as a ratio.
Next, there are 850 students attending the games. Write the proportion to start solving the problem.
Therefore, 357 middle school students attend the game.
A forest range discovered that 25% of the trees in his area were infected with a parasite. If there are 3060 trees in his area, how many trees are infected?
Then, divide by 100 to find the number of trees infected.
The answer is 765.
Therefore, there are 765 of the 3060 trees infected.
6. A small car company sold 65,000 cars last year. Ninety-five percent of those cars had airbags. How many cars had airbags?
12. A recent government survey shows that in New City, people spend 35% of their monthly income on rent. If average rent is $780, what is the average income?
13 A fluorescent light bulb uses 35% as much energy as an incandescent bulb. If an incandescent uses 75 watts, how much does the fluorescent use?
14. An average human weighs 160 pounds. An elephant weights 1500% more. How much does the elephant weigh?
15. An average elephant eats about 350lbs of food per day. Using your calculation from problems #14, what percent of its own weight does it consume each day?
To see the Review answers, open this PDF file and look for section 5.6.