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11 March, 09:21

When a group of students are seated 3 to a bench in an auditorium, 18 are left standing. If they were seated 4 to a bench, 3 benches would be empty. Find the number of benches and students

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  1. 11 March, 09:36
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    x = students

    b = benches

    when 3 are on a bench and 18 are standing the equation is:

    x = 3b+18

    when 4 are sitting and 3 benches are empty the formula is

    and x = 4b-12

    so 3b+18 = 4b-12

    rearrange to

    4b-3b = 18 + 12

    so b = 30

    now plug that into the first formula

    x=3 (30) + 18 = 108

    so 108 students and 30 benches
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