Math

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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?

  • Math -

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

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