SOLUTION: 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 ca

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

RELATED QUESTIONS
Karin made pressed cider with a group of campers. They wanted the counselors to have... (answered by checkley77)

All but 4 of the counselors at a certain summer camp have a sailing certification, first... (answered by richwmiller)

At a summer camp there is one counselor for every 8 campers. Write a direct variation... (answered by stanbon)

Two campers left the camp at 8:00 AM to paddle their canoe 10 Km upstream to a fishing... (answered by mananth)

Mr. Groff's class has more than 20 students but fewer than 30. The class was split into 5 (answered by ikleyn)

At camp last summer, the ratio of boys to girls was 5:4. If there was a total of 90... (answered by ptaylor)

At a summer camp there is one counselor for every 9 campers. Determine whether there is a (answered by rwm)

A summer camp wants to hire counselors and aides to fill its staffing needs at minimum... (answered by ikleyn)

Tong and Phillip are working as counselors in a day camp for kids. One of their tasks is... (answered by Theo)