A group of N students, where N < 50, is on a field trip. If their teacher puts them in groups of 8, the last group has 5 students. If their teacher instead puts them in groups of 6, the last group has 3 students. What is the sum of all possible values of N?
+130561 A group of N students, where N < 50, is on a field trip. If their teacher puts them in groups of 8, the last group has 5 students. If their teacher instead puts them in groups of 6, the last group has 3 students. What is the sum of all possible values of N?
We have this system
N = 8m + 5
N = 6n + 3 subtracting the second equation from the first gives
8m - 6n + 2 = 0 → 8m = 6n - 2
The possible solutions for m. n are
{ 2, 3} and {5, 7}
So.....N = 21 or N = 45
And the sum of all possible values of N = 21 + 45 = 66
