Question

The Chess club has 16 members and gains A new member every month. The film club has four members and gains four new members every month. Write and solve a system of equations to find when the member members in both clubs will be equal

Answer 1

Answer:

 16 + x  = 4 + 4x  is the required equation representing the situation.

After 4 months both the clubs will have SAME NUMBER of members.

Step-by-step explanation:

Let us assume in x months, both clubs will have same number of members.

The present members in chess club =  16

Gains a new member every month.

So, the members gained in  x months = x  (1)  = x

So, the Total members in Chess Club after x months

= Previous Members  + Addition in  x months   = 16 +x

The present members in Film club = 4

Gains a 4 member every month.

So, the members gained in  x months = x  (4)  = 4x

So, the Total members in Film Club after x months

= Previous Members  + Addition in  x months   =  4 +  4x

Now, according to question:

After x months both clubs have same members.

⇒  16 + x  = 4 + 4x

or, 16 - 4 = 4x- x

or, 3 x  = 12

⇒ x = 12/ 3  = 4 , or x  = 4

Hence, after 4 months both the clubs will have SAME NUMBER of members.