a) To model the total cost, \( y \), as a function of the number of rings purchased, \( x \), we can break down the costs as follows:
- The cost to play the game is a fixed amount of $2.
- The cost for each ring is $0.35. Therefore, if \( x \) is the number of rings purchased, the cost for the rings is \( 0.35x \).
Putting this together, the equation that models the total cost is:
\[ y = 2 + 0.35x \]
b) To find the total cost to play when purchasing 8 rings, we can substitute \( x = 8 \) into the equation:
\[ y = 2 + 0.35(8) \]
Calculating the cost for the rings:
\[ 0.35 \times 8 = 2.80 \]
Now substitute that value back into the equation:
\[ y = 2 + 2.80 = 4.80 \]
Therefore, the total cost to play if you purchase 8 rings is $4.80. This result is justified by substituting the number of rings into the cost equation and calculating the total cost based on the fixed entry fee and the variable cost per ring.
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