Question

Mr. Wallace needs to divide his class or 23 students into 9 groups. Each group can have two or three students. If a is the number or groups of 2 and b is the number of groups of 3, what system of equations could Mr. Wallace use to solve this problem ?

Answer 1

d) Mr.Wallace can use the following equations:

a + b = 9

2 a + 3 b = 23

Explanation:

Here, the total number of students = 23

Number of groups = 9

Each group can have 2 or 3 students.

a is the number of groups of 2.

⇒ Total students in a groups = a x (Number of student in each group)

= a x 2 = 2 a

b is the number of groups of 3

⇒ Total students in b groups = b x (Number of student in each group)

= b x 3 = 3 b

So, according to the question:

Total number of groups formed = 9

⇒ a + b = 9

Total number of students = 23

or Number of students in ( a group + b group ) = 23

⇒ 2 a + 3 b = 23

Hence, Mr.Wallace can use the following equations:

a + b = 9

2 a + 3 b = 23