Delilah wants to join a gym so she shops around to find the

Delilah wants to join a gym, so she shops around to find the one with the lowest overall price She finds that Gym A is running a special and only charges an $17 initiation fee plus $27 a month to be a member. Gym B charges $107 to join, and has a monthly fee of $21. Under what conditions would it be more expensive to join Gym B?

More than 12 months

Less than 12 months

More than 15 months

Less than 15 months

Solution

Here we will use trial and error method to find the best possible answer.

lets assume for 12 months.

Gym A charges $17 initiation fee plus $27 a month.

If Delilah joins a gym A for 12 month she needs to pay $17 + ($27*12) = 341

Gym A charges $107 join fee plus $21 a month.

If Delilah joins a gym B for 12 month she needs to pay $107 + ($21*12) = 359

now let assume for 15 months

Gym A charges $17 initiation fee plus $27 a month.

If Delilah joins a gym A for 15 month she needs to pay $17 + ($27*15) = 422

Gym A charges $107 join fee plus $21 a month.

If Delilah joins a gym B for 15 month she needs to pay $107 + ($21*15) = 422

so if she joins any Gym for 15 months then it will costs same for her.

now we will check for 14 months

Gym A charges $17 initiation fee plus $27 a month.

If Delilah joins a gym A for 14 month she needs to pay $17 + ($27*14) = 395

Gym A charges $107 join fee plus $21 a month.

If Delilah joins a gym B for 14 month she needs to pay $107 + ($21*14) = 401

so we can say that is she joins gym B for less than 15 months it will be more expensive