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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineKeenan and Darell went to an arcade where the machines took tokens. Keenan played 1010 games of skee ball and 66 games of pinball, using a total of 2828 tokens. At the same time, Darell played 88 games of skee ball and 44 games of pinball, using up 2020 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.\newlineKeenan and Darell went to an arcade where the machines took tokens. Keenan played 1010 games of skee ball and 66 games of pinball, using a total of 2828 tokens. At the same time, Darell played 88 games of skee ball and 44 games of pinball, using up 2020 tokens. How many tokens does each game require?\newlineEvery game of skee ball requires _\_ tokens, and every game of pinball requires _\_ tokens.
  1. Define variables: Let's define two variables: let xx be the number of tokens required for a game of skee ball, and yy be the number of tokens required for a game of pinball. We can then write two equations based on the information given:\newlineFor Keenan: 10x+6y=2810x + 6y = 28\newlineFor Darell: 8x+4y=208x + 4y = 20
  2. Use elimination method: To use elimination, we want the coefficients of one of the variables to be the same (or opposites) in both equations. We can achieve this by multiplying the second equation by 1.51.5 to match the coefficients of yy in the first equation:\newline1.5(8x+4y)=1.5(20)1.5(8x + 4y) = 1.5(20)\newlineThis gives us: 12x+6y=3012x + 6y = 30
  3. Eliminate y: Now we have a new system of equations:\newline10x+6y=2810x + 6y = 28\newline12x+6y=3012x + 6y = 30\newlineWe can eliminate y by subtracting the first equation from the second:\newline(12x+6y)−(10x+6y)=30−28(12x + 6y) - (10x + 6y) = 30 - 28\newlineThis simplifies to:\newline2x=22x = 2
  4. Solve for x: Dividing both sides of the equation by 22 gives us the value of xx:2x2=22\frac{2x}{2} = \frac{2}{2}x=1x = 1So, each game of skee ball requires 11 token.
  5. Substitute xx into equation: Now that we know the value of xx, we can substitute it back into one of the original equations to find the value of yy. We'll use the first equation:\newline10(1)+6y=2810(1) + 6y = 28\newline10+6y=2810 + 6y = 28
  6. Solve for yy: Subtracting 1010 from both sides gives us:\newline6y=28−106y = 28 - 10\newline6y=186y = 18
  7. Solve for y: Subtracting 1010 from both sides gives us:\newline6y=28−106y = 28 - 10\newline6y=186y = 18 Dividing both sides by 66 gives us the value of yy:\newline6y6=186\frac{6y}{6} = \frac{18}{6}\newliney=3y = 3\newlineSo, each game of pinball requires 33 tokens.

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