An amusement park offers two options. Option 1 involves a $10 admission fee plus $0.50 per ride. Option 2 involves a $6 admission fee plus $0.75 per ride. For how many rides do the two options have the same cost ( or, what is the break-even point)?

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wifilethbridge wifilethbridge · Answer 1 · 2019-02-22T06:30:07+01:00

Answer:

16 rides

Step-by-step explanation:

Option 1 . Admission fee = $10

Each ride = $0.50

Option 2 . Admission fee = $6

Each ride = $0.75

Let no. of rides be x

So, cost of ride according to option 1 = 0.50x

So, total cost after having x rides according to option 1 :

= 10+0.50x ---1

Cost of ride according to option 2 = 0.75x

So, total cost after having x rides according to option 2 :

= 6+0.75x --2

Now to find the beak even point i.e. having the same cost

Equate 1 and 2

[tex]10+0.50x=6+ 0.75x[/tex]

[tex]10-6= 0.75x-0.50x[/tex]

[tex]4= 0.25x[/tex]

[tex]\frac{4}{0.25} =x[/tex]

[tex]16=x[/tex]

Thus for 16 rides , the two options have the same cost .

Hence the break even point is 16 rides