Respuesta :
We have here two equations that we need to determine in order to solve the question.
First, we have:
1. If you pay $80 for a monthly pass and then you pay $5 for each visit.
2. You can pay $15 for each visit with no monthly pass.
In the first case, the expression that translates that in an equation is:
[tex]y=80+5x[/tex]In the second case, the expression is:
[tex]y=15x[/tex]Since y is the total cost to go to the gym, and we need to know what the cost is when either option cost the same, we can equate both equations as follows:
[tex]y=80+5x,y=15x\Rightarrow80+5x=15x[/tex]Then, we need to solve the last equation subtracting 5x to both side of it:
[tex]80+5x-5x=15x-5x\Rightarrow80=10x\Rightarrow\frac{80}{10}=\frac{10}{10}x\Rightarrow x=8[/tex]Thus, the value for x is 8. To find the value of the cost, we can substitute this value in either equation. The cost will be the same:
[tex]y=80+5\cdot(8)\Rightarrow y=80_{}+40\Rightarrow y=120[/tex]Or
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