The director of a marching band asks the band members to line up in rows of four, but one is left over. Then she tries to line them up in rows of six, but three are left over. Finally, she tries to line them up in rows of seven, but four are left over. The band has fewer than 100 members. How many members are there?

Question

Mathematics

Allen Gregory

24 December, 03:55

The director of a marching band asks the band members to line up in rows of four, but one is left over. Then she tries to line them up in rows of six, but three are left over. Finally, she tries to line them up in rows of seven, but four are left over. The band has fewer than 100 members. How many members are there?

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Rodney Harrington · Answer 1

There are 81 band members. : - )

4 rows of 20 = 80 ... with one left over = 80 + 1 (81)

6 rows of 13 = 78 ... with three left over = 78 + 3 (81)

7 rows of 11 = 77 ... with four left over = 77 + 4 (81)