System word problem (algebra)

Question

The chess club has 16 members and gains a new member every month. The film club has 4 members and gains 4 new members every month. When will the number in both clubs be equal?

Answer 1

Create an equation from the words describing the two groups. Let m = the number of months for which both clubs are adding new members.

 

For chess, the total membership would be 16 plus an expression for how many new members will be added, i.e., the number added each month times the number of months or 1 x m. So 16 + m.

 

For film, do the same: 4 + 4m

 

The question asks when will the two total memberships be equal, so set the two expressions equal to each other:

 

16 + m = 4m + 4

 

16 = 3m + 4  subtracting m from both sides

 

12 = 3m  subtracting 4 from both sides

 

4 = m dividing both sides by 3  (ANSWER)

 

To check your answer, plug in the value 4 for m in the main equation.  If you get a true statement, the solution is correct.  After 4 weeks, both clubs will have 20 members.

Answer 2

16+x=4+4x

12=3x

4=x

They will be equal in 4 months