SOLUTION: a rock climbing gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited rock climbing and $6 per day f

Algebra ->  Expressions-with-variables -> SOLUTION: a rock climbing gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited rock climbing and $6 per day f      Log On


   

Question 159781: a rock climbing gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited rock climbing and $6 per day for equipment rental. Write and solve an equation to find how many times you must use the gym to justify becoming a member.
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

RATE 1:
charge per session + equip't rental
$16/day + $8/day
RATE 2:
unlimited session + equip't rental
$450/yr + $6/day
Remember: x=no.of times (session) going to the gym
.
So equating RATE 1 & RATE 2:
16x%2B8x=450%2B6x
24x-6x=450
18x=450 --------> cross%2818%29%2Fcross%2818%29=cross%28450%2925%2Fcross%2818%29
x=25, number of sessions to go should be MORE than this in order to justify of becoming a member.
Let's see why?
RATE 1: =16%2A25%2B8%2A25
= 400%2B200
= $600
RATE 2: = 450%2B6%2A25
= 450%2B150
= 600
You see, if go 25 sessions, either RATE is okay. But if you go over 25, then RATE 2 is a better choice for unlimited rock climbing. Try 30 sessions you'll see.
Thank you
Jojo