11.2 Comparing Different Quantities

You will often need to compare groups that are different sizes.
In this case, it'll be easy if you use percentages.

                                  
I have three questions to ease your understanding.

Questions

1. There were 270 people in cinema. There were 168 women and 102 men. There were 152 people in a theatre. Theatre were 78 women and 74 men.

a. Work out the percentage of women in each venue.
b. Work out the percentage of men in each venue.

a) cinema: 168/270*100% = 62%
    theatre: 78/152*100% = 51%

b) cinema: 102/270*100% = 37%
     theatre: 74//152*100% = 49%

2. In Alphatown there are 5400 young people aged 18 or less. There are 9300 aged over 18. in Betatown there are 9300 young people aged 18 or less. There are 21600 aged over 18.

a. Calculate the percentage of young people in each town.
b. Which town has the greater proportion of young people?

a)
 Alphatown:  5400/14700*100% = 37% {5400 is the amount of young people, 14700 is the amount of all people.}
Betatown: 9300/30900*100% = 30%

b) Alphatown: 37%
    Betatown:  30%

= Alphatown.

3. This table shows the result of a survey in a factory.

a. What percentage of men are smokers?
b. Compare the percentages of men and women who are non-smokers.

a) 12/76*100% = 16%
b) Men: 64/76*100% = 84%
    Women: 32/41*100% = 78%