How to solve systems by substitution: word problems

Question

A gym charges a one-time registration fee as well as a monthly fee. The cost of joining the gym for 4 months is $370, and the cost of joining for 6 months is $530. Write and solve a system of equations to find the registration fee and monthly fee.

Answer 1

530=r+6f

370=r+4f

subtract

160=2f

f=160/2

f=$80 for the monthly fee

370=r+4(80)

370=r+320

r=370-320=$50 for the registration fee

 

if you need to use substitution...

530=r+6f

370=r+4f ------>r=370-4f

substitute

530=370-4f+6f

530-370=2f

160=2f

f=160/2=$80 again

and so on...