Students can use the local gym for $5 per visit, or they can get

Question

Students can use the local gym for $5 per visit, or they can get a weekly pass for $13 and then visit the gym for $1 per visit. What is the minimum number of times a student needs to visit the gym per week for the weekly pass to be worth it?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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bhavikachawla97 · Answer

We want the weekly pass to be worth it, i.e., cost less than or equal to pay-per-visit:

13+x ≤5x
13+x≤5x
Solving for x,
x=3.25

Since x must be a whole number, the minimum number of visits is 4

ManifestDreamMBA · Answer

Let number of days be n
5n>=13+n
4n>=13
n>=13/4
n>=3.25

We need the number of days as charges are for full day
n (min) = 4

Ayeka · Answer

13+x<=5x
13<=4x
3.25<=x 
x is more than 3.25, so minimum number of days for the weekly pass to be worth it is 4 days.

Answer: D

kingbucky · Answer

Let us say, after n days, it becomes more economical (cost less) to use the weekly pass,  ie,  we will have:
13+n(1) <= n(5)  
 i.e.  13 <= 4(n) 
 i.e.   3.25 <= n
 i.e.  any value of n that is greater than 3.25 will satisfy our constraints, additionally n(number of days takes only integer values) Hence, the minimum value of n where weekly pass is cheaper than daily pass is  4

DiveshR · Answer

Does worth it mean "greater than" or "greater than or equal to"?

Bunuel · Answer

In this context,  "worth it" means the weekly pass costs the same or less , so it corresponds to  "less than or equal to"  the cost of paying per visit.

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