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.

x − re g i s t r a t i o n f ee y − m o n t h l y f ee { x + 6 y = 530 ∣ ∗ ( − 1 ) x + 4 y = 370 ​ { − x − 6 y = − 530 x + 4 y = 370 ​ + − − − − − A dd i t i o n − 2 y = − 160 ∣ d i v i d e b y − 2 y = 80 x = 370 − 4 y = 370 − 4 ∗ 80 = 370 − 320 = 50 R e g i s t r a t i o n f ee i s e q u a l t o 50$ an d m o n t h l y f ee i s e q u a l t o 80$.

Answered by luana | 2024-06-10

The registration fee is $50 and the monthly fee is $80. This was determined by setting up and solving a system of equations based on the costs for different months. The equations were derived from the information about the gym's fees for 4 and 6-month memberships.
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Answered by luana | 2024-09-30