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Answer :
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.
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.
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