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Answer :
To solve the problem, we need to find the equation that represents the yearly cost for a nonmember at the video game arcade based on the total number of game tokens purchased.
1. Understand Nonmember Costs:
- A nonmember pays $0.20 per game token.
- Therefore, if a nonmember buys [tex]\( x \)[/tex] game tokens, their total cost for the year would be calculated by multiplying the number of tokens by the cost per token.
2. Set Up the Equation:
- The cost for a nonmember is calculated as:
[tex]\[
y = 0.20 \times x
\][/tex]
- This means for every game token purchased, the cost is 20 cents, so the equation shows that the total cost increases linearly with the number of tokens.
3. Verify Given Equation:
- We are given the equation [tex]\( y = \frac{1}{5} x \)[/tex].
- Let's simplify [tex]\( \frac{1}{5} \)[/tex]:
- [tex]\( \frac{1}{5} \)[/tex] is equivalent to 0.20 when converted into decimal form.
- Therefore, the given equation [tex]\( y = \frac{1}{5} x \)[/tex] matches [tex]\( y = 0.20 \times x \)[/tex], confirming it accurately represents the nonmember's yearly cost at the arcade.
By comparing both representations, we conclude that the equation [tex]\( y = \frac{1}{5} x \)[/tex] correctly represents the yearly cost for a nonmember, as it aligns with the 20 cents per token charge.
1. Understand Nonmember Costs:
- A nonmember pays $0.20 per game token.
- Therefore, if a nonmember buys [tex]\( x \)[/tex] game tokens, their total cost for the year would be calculated by multiplying the number of tokens by the cost per token.
2. Set Up the Equation:
- The cost for a nonmember is calculated as:
[tex]\[
y = 0.20 \times x
\][/tex]
- This means for every game token purchased, the cost is 20 cents, so the equation shows that the total cost increases linearly with the number of tokens.
3. Verify Given Equation:
- We are given the equation [tex]\( y = \frac{1}{5} x \)[/tex].
- Let's simplify [tex]\( \frac{1}{5} \)[/tex]:
- [tex]\( \frac{1}{5} \)[/tex] is equivalent to 0.20 when converted into decimal form.
- Therefore, the given equation [tex]\( y = \frac{1}{5} x \)[/tex] matches [tex]\( y = 0.20 \times x \)[/tex], confirming it accurately represents the nonmember's yearly cost at the arcade.
By comparing both representations, we conclude that the equation [tex]\( y = \frac{1}{5} x \)[/tex] correctly represents the yearly cost for a nonmember, as it aligns with the 20 cents per token charge.
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