ratios and percents

Problem 6.2: Nine out of every eleven dentists in my city say you shouldn't eat candy and the rest say it's OK to eat candy. Eighteen dentists in my city say that it's OK to eat candy. How many dentists are in my city? 

• 81

• 89

• 99

• 22

Answer explanation

Solution 2: Consider groups of 11. We are told that 9 out of every 11 dentists say you shouldn't eat candy. Therefore, 2 out of 11 dentists say it's OK to eat candy. Suppose we place all the dentists in the city in groups of 11 such that 9 of them say you shouldn't eat candy and the other 2 say it's OK. Since there are 18 dentists who say it's OK to eat candy, we'll need 18/2 = 9 groups of dentists. There are 11 
dentists in each group, for a total of 11(9) = 99 dentists.

Problem 6.3: Consider the pet store in which the ratio of dogs to cats to mice is 2 : 3 : 30. Dogs, cats, and mice are the only animals in the store. If there are 385 animals in the store, how many cats are in the store? 

• 33

• 35

• 45

• 32

Answer explanation

Solution 2: We can use the ratio information to group the animals. As we noted earlier, for every 2 dogs, there are 3 cats and 30 mice. Therefore, we group the animals such that each group contains 2 dogs, 3 cats, and 30 mice. Each such group has 2 + 3 + 30 = 35 animals, and there are 385 total animals, so there must be 11 groups. There are 3 cats in each of these groups, so there are 11 x 3 = 33 cats. 

The ratio of men to women in Smalltown is 3 : 2. The population of Bigtown is three times as

large as that of Smalltown, and the ratio of men to women in Bigtown is 2 : 3. If Smalltown and Bigtown

are combined, what is the ratio of men to women in the combination?

• 11/9

• 11/5

• 9/11

• 9/5

Select two of following ratios that are NOT equivalent to 20:24?

• 10:12

• 5:6

• 4:6

• 16:20

Select ALL the ratios that are equivalent to 16 : 6

• 3 to 8

• 32 : 12

• 4 to 2

• 8 to 3

• yes

• no

The ratio of boys to girls in the musical is 15 to 45. What is the ratio of girls to total students in the musical?

• 15 to 60
• 15 to 45
• 45 to 60
• 45 to 15

Danika increased the amount of protein she eats every day from 48g to 54g. By what percentage did Danika increase the amount of protein she eats?

• 11.1%

• 12.5%

• 88.9%

• 112.5%

Mr. Layton’s 2nd period class has 14 boys and 21 girls. What percent of the class is boys?

• 67%

• 40%

• 60%

• 14%

In 1999, the price of unleaded fuel was $1.09.  In 2015, the price of unleaded fuel is $1.89.  What is the percent change?

• 173% increase
• 73% increase
• 73% decrease
• 27% increase