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

$x-\ registration\ fee\\ y-\ monthly\ fee\\\\ \left \{ {{x+4y=370} \atop {x+6y=530\ \ |*(-1)}} \right. \\\\ \left \{ {{x+4y=370} \atop {-x-6y=-530}} \right. \\+-----\\Addition\\\\ -2y=-160\ \ | divide\ by\ -2\\ y=80\\\\ x=370-4y=370-4*80=370-320=50\\\\ Registration\ fee\ is\ equal\ to\ 50\ \ and\ monthly\ fee\ is\ equal\ to\ 80\ .$