Mrs. Jones has a prime number of children in her class. When she divides the children into teams of 7, one team has 6. When she divides the children into teams of 6, one team has 5. How many children are in the class?

Answer 1

x/7 = A 6/7 = (7 A + 6)/7
x/6 = B 5/6 = (6 B + 5)/6

so x = 7 A + 6
and x= 6 B + 5

7 A +6 = 6 B + 5

6 B - 7 A = 1

what multiples of 7 and 6 differe by one?
35 and 36 or 48 and 49 ?
try 35 and 36
A = 5 and B = 6
x = 6 B + 5 = 41
or
x = 7 A + 6 = 41 sure enough