Question 201020: During a recent survey of 2 classes, 1/3 of the students bring their lunch to school, 1/4 buy their lunch, and 1/6 go home. The remaining 18 students don't eat lunch. How many students are in the 2 classes?
My niece answered 116. Please verify if this correct, so I can double check our work, it has been several since my Algebra days. Thanks, Cindy
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Right off the bat you can tell that 116 is not correct. 116 is not evenly divisible by either 3 or 6, so you would have a fractional part of a student bringing their lunch and another fractional part of a student going home. Basically, someone's head and shoulders went home and the rest of their body stayed at school and ate the lunch they brought.
Let  represent the number of students in the two classes. One third of them bring their lunch,  , one fourth of them buy,  , one-sixth go home,  , and 18 don't eat lunch. And the sum of all these pieces is , so:
The lowest common denominator of 3, 4, and 6 is 12, so multiply both sides of the equation by 12:
)
Collect terms:
)
Add  to both sides:
Multiply both sides by 
Check the answer: One-third of 72 is 24, one-fourth of 72 is 18, one-sixth of 72 is 12. 24 plus 18 plus 12 plus 18 is 72. Answer checks.
John
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