Question

A health club charges non-members $5 per day to swim and $9 per day for an exercise class. Members pay a yearly fee of $300 plus $4 per day to attend an exercise class and no swim fee. If Robert swims and takes an exercise class every time he goes to the gym, which equation shows the number of days he must use the gym to make the membership worthwhile?

Answer 1

let x be the number of days

if he has a membership, the cost is P(x)= 300 + 4 x
if he doesnt, it's C(x)=(5+9)x=14x

we can make them equal to each other and solve for x, to find the days where price is the same for both scenarios.

14x=300+4x

x=30

This means that he must use the membership 30 days a month to make it worthwhile.
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you should also check if the answer makes sense.

P(x)= 300 + 4 x
C(x)=14x

x=29, x 31

P(29)=416
C(29)=406

no membership is cheaper

P(31)=424
C(31)=434

membership is cheaper

Answer 2

Thank You So Much

Answer 3

no problem