M3L3 Application Problem

Question

One ninth of the students in Mr. Beck’s class list red as their favorite color. Twice as many students call blue their favorite, and three times as many students prefer pink. The rest name green as their favorite color. What fraction of the students say green or pink is their favorite color? 

Extension: If 6 students call blue their favorite color, how many students are in Mr. Beck’s class?

Answer 1

To help understand this problem, remember that FRACTIONS are numerical quantities that are NOT whole numbers and if this problem you can assume that all the given fractions when added together will equal ONE.

So for the 1st part of the problem, the number of students doesn't really matter and you can set the sum of all the fractions to ONE.

Like RED + Like BLUE + Like PINK + Like GREEN = Total # of kids in Ms. Beck's class

SUM of the PARTS = WHOLE

¹/₉ + 2(¹/₉) + 3(¹/₉) + Remaining students who like GREEN = 1

To find out the remaining kids who like GREEN, solve for the missing fraction

Kids who like GREEN = 1 - ¹/₉ - 2(¹/₉) - 3(¹/₉)

Kids who like GREEN = 1 - ¹/₉ - ²/₉ - ³/₉

You can rewrite 1 as ⁹/₉ so that all the fractions have the same denominator and you can subtract

Kids who like GREEN = ⁹/₉ - ¹/₉ - ²/₉ - ³/₉

Kids who like GREEN = ³/₉ OR ¹/₃

And since you know that the kids that like PINK is 3(¹/₉) OR ³/₉ = ³/₉

The fraction of kids that like PINK or GREEN is ¹/₃ Final Answer

Extension, if 6 students like BLUE, then (²/₉)(X) = 6 ...where X is the total number of kids in the class. Solve for X

X = 9(6)/2 = 54 / 2 = 27 students Final Answer

You can check with all the other fractions given:

Kids that like RED = ¹/₉(27) = 3

Kids that like BLUE = 6

Kids that like PINK = ³/₉(27) = 9

Kids that like GREEN = ¹/₃(27) = 9

Total = 3 + 6 + 9 + 9 = 27

Hope this helps... :)

Answer 2

1/9 red

2/9 blue

3/9 pink

9/9 - 6/9 = 3/9 green

green or pink, 3/9 + 3/9 = 6/9