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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineJordan and Donald went to an arcade where the machines took tokens. Jordan played 11 game of skee ball and 77 games of pinball, using a total of 2323 tokens. At the same time, Donald played 22 games of skee ball and 33 games of pinball, using up 1313 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 elimination, and fill in the blanks.\newlineJordan and Donald went to an arcade where the machines took tokens. Jordan played 11 game of skee ball and 77 games of pinball, using a total of 2323 tokens. At the same time, Donald played 22 games of skee ball and 33 games of pinball, using up 1313 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 ss and for a game of pinball as pp. Jordan played 11 game of skee ball and 77 games of pinball, using a total of 2323 tokens. This gives us the equation s+7p=23s + 7p = 23.
  2. Jordan's Games and Tokens: Donald played 22 games of skee ball and 33 games of pinball, using up 1313 tokens. This gives us the equation 2s+3p=132s + 3p = 13.
  3. Eliminate Variable ss: We now have a system of two equations. We need to eliminate one of the variables, ss or pp. We choose to eliminate ss because its coefficients are 11 and 22, which are easier to work with.
  4. Multiply and Subtract Equations: To eliminate ss, we multiply the first equation by 22, the coefficient of ss in the second equation. This gives us the new equation 2s+14p=462s + 14p = 46.
  5. Solve for pp: We now subtract the second equation from the new first equation to eliminate ss. This gives us 11p=3311p = 33.
  6. Substitute pp into Equation: Solving for pp, we divide both sides of the equation by 1111, which gives us p=3p = 3.
  7. Final Solution: We substitute p=3p = 3 into the first equation and solve for ss. This gives us s+7(3)=23s + 7(3) = 23, which simplifies to s+21=23s + 21 = 23.
  8. Final Solution: We substitute p=3p = 3 into the first equation and solve for ss. This gives us s+7(3)=23s + 7(3) = 23, which simplifies to s+21=23s + 21 = 23. Subtracting 2121 from both sides of the equation, we get s=23−21s = 23 - 21, which gives us s=2s = 2.

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