The yearly cost in dollars, [tex] y [/tex], for a member at a video game arcade based on the total game tokens purchased, [tex] x [/tex], is given by the equation:

[tex] y = \frac{1}{10} x + 60 [/tex]

A nonmember pays \$0.20 per game token but no yearly fee.

Which equation represents the yearly cost for a nonmember at the same video game arcade based on the total number of game tokens purchased in a year?

A. [tex] y = \frac{1}{2} x [/tex]

B. [tex] y = \frac{1}{10} x + 60 [/tex]

C. [tex] y = \frac{1}{5} x [/tex]

D. [tex] y = \frac{1}{20} x + 80 [/tex]

To determine which equation represents the yearly cost for a nonmember based on the total number of game tokens purchased, let's break down the problem step-by-step.

1. Understanding the nonmember cost structure:
- A nonmember pays $0.20 per game token.
- There is no yearly fee for nonmembers.

2. Formulating the cost equation for a nonmember:
- The cost for a nonmember is only dependent on the number of tokens purchased.
- If "x" is the number of game tokens, then the total cost "y" for a nonmember would be:
[tex]\[
y = 0.20 \times x
\][/tex]

3. Converting the cost equation into the given multiple-choice format:
- The equation [tex]$ y = 0.20 \times x $[/tex] can be rewritten using a fraction for clearer comparison.
- Since [tex]$ 0.20 $[/tex] is equivalent to the fraction [tex]$ \frac{1}{5} $[/tex], the equation becomes:
[tex]\[
y = \frac{1}{5}x
\][/tex]

4. Matching with the given options:
- Let's compare this equation with the options provided:
- [tex]$ y = \frac{1}{2} x $[/tex]
- [tex]$ y = \frac{1}{10} x + 60 $[/tex]
- [tex]$ y = \frac{1}{5} x $[/tex] ⟵ This matches our derived equation.
- [tex]$ y = \frac{1}{20} x + 80 $[/tex]

Thus, the correct equation that represents the yearly cost for a nonmember is [tex]$ y = \frac{1}{5} x $[/tex], which is the third option.