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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTrisha loves riding Ferris wheels and roller coasters. While visiting the Scott County Fair, she first went on the Ferris wheel 11 time and the roller coaster 11 time, using a total of 66 tickets. Then, after taking a break and having a snack, Trisha went on the Ferris wheel 44 times and the roller coaster 22 times, using a total of 1616 tickets. How many tickets does it take to ride each attraction?\newlineIt takes _\_ tickets to ride the Ferris wheel, and _\_ tickets to ride the roller coaster.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTrisha loves riding Ferris wheels and roller coasters. While visiting the Scott County Fair, she first went on the Ferris wheel 11 time and the roller coaster 11 time, using a total of 66 tickets. Then, after taking a break and having a snack, Trisha went on the Ferris wheel 44 times and the roller coaster 22 times, using a total of 1616 tickets. How many tickets does it take to ride each attraction?\newlineIt takes _\_ tickets to ride the Ferris wheel, and _\_ tickets to ride the roller coaster.
  1. Define Equations: Let's denote the number of tickets needed for one ride on the Ferris wheel as ff and for the roller coaster as rr. Trisha's first round of rides gives us the equation f+r=6f + r = 6.
  2. Second Round Rides: Trisha's second round of rides, where she went on the Ferris wheel 44 times and the roller coaster 22 times, gives us the equation 4f+2r=164f + 2r = 16.
  3. Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, ff or rr. We choose to eliminate rr because its coefficients are the same in both equations.
  4. Multiply and Subtract: To eliminate rr, we multiply the first equation by 22 to match the coefficient of rr in the second equation. This gives us the new equation 2f+2r=122f + 2r = 12.
  5. Solve for Ferris Wheel: We now subtract the first new equation from the second equation to eliminate rr. This gives us 4f+2r−(2f+2r)=16−124f + 2r - (2f + 2r) = 16 - 12, which simplifies to 2f=42f = 4.
  6. Substitute and Solve: Solving for ff, we divide both sides of the equation by 22, giving us f=2f = 2. This means it takes 22 tickets to ride the Ferris wheel.
  7. Substitute and Solve: Solving for ff, we divide both sides of the equation by 22, giving us f=2f = 2. This means it takes 22 tickets to ride the Ferris wheel.We substitute f=2f = 2 into the first equation and solve for rr. This gives us 2+r=62 + r = 6, which simplifies to r=4r = 4. This means it takes 44 tickets to ride the roller coaster.

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