Chapter CSB1.2, Problem 31E

a.

To determine

To find: the greatest number of students that could be in each row.

Answer to Problem 31E

12

Explanation of Solution

Given information: In the parade, 36 members of the color guard are to march in front of 120 members of high school marching band.

In order to find the greatest number of students that could be in each row, we have to find H.C.F of 36 and 120.

The factors of 36=1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 120=1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40…………………………

H.C.F.(Highest common factor) = 12

Hence the greatest number of students that could be in each row = 12

b.

To determine

To find: the number of rows that each group will have.

Answer to Problem 31E

Band of 36 members will have 3 rows.

Band of 120 members will have 10 rows.

Explanation of Solution

Given information: In the parade, 36 members of the color guard are to march in front of 120 members of high school marching band.

Since each row have 12 members then number of rows in band of 36 members = $\frac{36}{12}=3$

Since each row have 12 members then number of rows in band of 120 members = $\frac{120}{12}=10$