Question

A choir is performing for the school fall festival. On the first night 12 choir members were missing so they stood in 5 equal rows. On the sencond night, 1 member was missing so they stood in 6 even rows. How many choir members are there?

Answer 1

Let N=number of choir members.
Then for the first night,
N=5m+12
for the second night,
N=6n+1

We look for the smallest number which when divided by 5 gives a remainder of 2, and when divided by 6 gives a remainder of 1.

Possible values:
N=17,22,27,32,<b>37</b>,42,47,52,57,62,<b>67</b>,72,...
N=7,13,19,25,31,<b>37</b>,43,49,55,61,<b>67</b>,72
So the minimum number of choir members is 37. Other possibilities are 67,97,127,...