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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineClarence and Angie went to an arcade where the machines took tokens. Clarence played 66 games of skee ball and 22 games of pinball, using a total of 1212 tokens. At the same time, Angie played 66 games of skee ball and 55 games of pinball, using up 2121 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires __\_\_ tokens, and every game of pinball requires __\_\_ tokens.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineClarence and Angie went to an arcade where the machines took tokens. Clarence played 66 games of skee ball and 22 games of pinball, using a total of 1212 tokens. At the same time, Angie played 66 games of skee ball and 55 games of pinball, using up 2121 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires __\_\_ tokens, and every game of pinball requires __\_\_ tokens.
  1. Denote tokens for games: Let's denote the number of tokens required for a game of skee ball as xx and for a game of pinball as yy. Clarence's games can be represented by the equation: 6x+2y=126x + 2y = 12. Angie's games can be represented by the equation: 6x+5y=216x + 5y = 21.
  2. System of equations: We now have a system of equations:\newline6x+2y=126x + 2y = 12 (Equation 11)\newline6x+5y=216x + 5y = 21 (Equation 22)\newlineWe can use either substitution or elimination to solve this system. Let's use elimination.
  3. Elimination method: To eliminate xx, we can subtract Equation 11 from Equation 22: (6x+5y)−(6x+2y)=21−12(6x + 5y) - (6x + 2y) = 21 - 12 6x+5y−6x−2y=21−126x + 5y - 6x - 2y = 21 - 12 3y=93y = 9
  4. Solve for y: Divide both sides of the equation by 33 to solve for y: \newline3y3=93\frac{3y}{3} = \frac{9}{3}\newliney=3y = 3
  5. Substitute back for x: Now that we have the value for yy, we can substitute it back into Equation 11 to solve for xx:6x+2(3)=126x + 2(3) = 126x+6=126x + 6 = 12
  6. Solve for x: Subtract 66 from both sides of the equation to solve for x:\newline6x+6−6=12−66x + 6 - 6 = 12 - 6\newline6x=66x = 6
  7. Final solution: Divide both sides of the equation by 66 to solve for xx:6x6=66\frac{6x}{6} = \frac{6}{6}x=1x = 1

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