Difference between revisions of "2009 CEMC Gauss (Grade 8) Problems/Problem 18"
(Created page with "==Problem== In a class of <math>40</math> students, <math>18</math> said they liked apple pie, <math>15</math> said they liked chocolate cake and <math>12</math> said they did...") |
|||
| Line 23: | Line 23: | ||
~anabel.disher | ~anabel.disher | ||
| + | {{CEMC box|year=2009|competition=Gauss (Grade 8)|num-b=17|num-a=19}} | ||
Latest revision as of 21:28, 19 October 2025
Problem
In a class of 
students, 
said they liked apple pie, 
said they liked chocolate cake and 
said they did not like either. How many students in the class liked both?
Solution
Let 
be the number of students in the class that liked both apple pie and chocolate cake. This means that 
students liked apple pie but not chocolate cake, and 
students liked chocolate cake but not apple pie.
We can now add up the individual amounts for people that liked one, both, or neither, and set it equal to the number of students in the class, which is :
Adding numbers and like-terms together, we get:
Adding to both sides, we get:
Subtracting from both sides, we get:
~anabel.disher
| 2009 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| CEMC Gauss (Grade 8) | ||
