Band Word Problem

Question

The middle school band has 56 members.The high school band has 96 members.The bands are going to march one in front of the other at a parade. The director wants to arrange the bands into the same number of columns . What is the greatest number of columns in which the two bands can be arranged if each column has the same number of marchers?How many band members will be in each column?

Answer 1

find the GCF of 56 and 96

56=2x2x2x7

96=2x2x2x2x2x3

the GCF=2x2x2=8

there will be 8 columns

each column will contain 96/8=12 plus 56/8=7 equals 19 band members

Answer 2

Let's break these down to their prime numbers and see how many each band has in common:

56 = 8 * 7

56 = 4 * 2 * 7

56 = 2 * 2 * 2 * 7

 

96 = 16 * 6

96 = 4 * 4 * 6

96 = 2 * 2 * 4 * 6

96 = 2 * 2 * 2 * 2 * 6

96 = 2 * 2 * 2 * 2 * 2 * 3

 

If we take a look at both bands, they have three 2s in common.

2 * 2 * 2 = 8, so if the director wants them to have the same number of columns, then there will need to be 8 columns.

 

To solve the number of band members in each column, all you need to do is divide 56 and 96 each by 8.