Question 1133191: Brad, Chaz, Dean and Evie go swimming at the same pool. Brad goes every 3 days. Chaz every 6 days and Dean every 7 days. The four all meet up only once every 84 days.
How often does Evie go to the pool if she swims less often than any of the others?
A. 8 days
B. 10 days
C. 12 days
D. 14 days
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Ans: C. 12 days
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Brad 3
Chaz 6 = 2*3
Dean 7
The LCM is 3*2*7 = 42
84 / 42 = 2, hence Evie must go every 3*2*2 = 12 days
[ Note: NOT 7*2 = 14 because the LCM would still be 42, the solution requires the LCM be 84 ]
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Follow up to the student: the problem says "The four all meet up only once every 84 days," while the LCM of the periods given (for three of the four people) is 42. So the question is what is the periodicity of the fourth person? That fourth person must have an additonal factor of 84/42 = 2 in their periodicity, to make the LCM of all four people 84.
84 (the goal) = 2*2*3*7
42 (the given information) = 2*3*7
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84/42 = 2 = the missing factor needed.
Someone needs to go to the gym 1/2 as often as one of the others. To do this AND get an LCM of 84, you must multiply Chaz's periodicity by 2. For any of the others, an additional factor of "2" will result in a common factor of "2" to Chaz's periodicity and it won't change the LCM -- that is what my note was about).
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