At a party one hundred and twenty people danced. The girls all started dancing one after the other. Tina was first girl who danced with seven men,Reena the second girl who danced with eight men, Sheela the third girl who danced with nine and so on up to Raveena who danced with all the men present. How many men were present at the party ?

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  1. number of men --- m
    number of girls --- g
    m+g = 120

    Tina danced with 7 men
    Reena danced with 8 men
    Raveena danced with 120-g men

    this is an arithmetic sequence with a=7, d=1

    term(g) = m
    a + (g-1)d = m
    7 + g-1 = m
    g - m = -6
    also g+m = 120
    add them
    2g = 114
    g = 57
    m = 120-57 = 63

    There were 63 men and 57 girls

    last girl should have danced with 63 men
    ---> last term = 63
    term (57) = a + 56d = 7 + 56(1) = 63

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  2. thankyou so much

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