Problema Solution
Adams county and madison county are gathering groups of runners to run a relay race. Adams county recruits runners in group of 6 while madison county recruits runners in groups of 7. If both counties end up with the same number of runners, what is the smallest number of runners each must have recruited?
Answer provided by our tutors
let
a = the number of recruitment Adams county made, a is non negative integer
m = the number of recruitment Madison county made, m is non negative integer
6a = 7m
we need to find the smallest values from a and m such that 6a = 7m
Least Common Multiple of 6 and 7 is 42 thus for
a = 42/6 = 7
m = 42/7 = 6
6*7 = 7*6
the smallest number of runners that each must have recruited is 42.