Question

Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym after x months and spends the rest of the year, y months, with the second gym. The membership to the first gym costs $85 per month, while the membership for the second gym costs $50 per month. If she ended up spending a total of $705 over the course of the year, how much time did she spend at each gym?

Answer 1

Jan spent 3 months at the first gym and 9 months at the second gym.

Explanation:

Given that:

1 year = 12 months

x = months at gym one

y = months at other gym

According to given statement;

x+y=12 Eqn 1

85x+50y=705 Eqn 2

Multiplying Eqn 1 by 50

50(x+y=12)

50x+50y=600 Eqn 3

Subtracting Eqn 3 from Eqn 2

(85x+50y)-(50x+50y)=705-600

85x+50y-50x-50y=105

35x=105

Dividing both sides by 35

`(35x)/(35)=(105)/(35)\\x=3`

Putting x=3 in Eqn 1

3+y=12

y=12-3

y=9

Hence,

Jan spent 3 months at the first gym and 9 months at the second gym.