Question 338853: In summer camp, counselors split the campers into 3,5 or 6 equal groups, but always ended up with 1 extra camper. Today, they split the campers into 7 equal sized groups, and no campers were left over. What is the smallest number of campers at this camp?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! In summer camp, counselors split the campers into 3,5 or 6 equal groups,
but always ended up with 1 extra camper.
Today, they split the campers into 7 equal sized groups, and no campers were left over.
What is the smallest number of campers at this camp?
:
Find a number that is a multiple of 7 that is 1 more than a multiple of 5
the units digit will be 1 or 6
Divide that by 6 to see if the remainder is 1 (this also takes care of 3)
:
Multiple of 7, 49, 56, 63, 70, 77, 84, 91 Bingo!
:
91/7 = 13
91/6 = 15 Remainder 1
91/5 = 18 remainder 1
91/3 = 30 remainder 1
|
|
|
