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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineCandice loves riding Ferris wheels and roller coasters. While visiting the Lincoln County Fair, she first went on the Ferris wheel 44 times and the roller coaster 44 times, using a total of 3232 tickets. Then, after taking a break and having a snack, Candice went on the Ferris wheel 55 times and the roller coaster 22 times, using a total of 2525 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.\newlineCandice loves riding Ferris wheels and roller coasters. While visiting the Lincoln County Fair, she first went on the Ferris wheel 44 times and the roller coaster 44 times, using a total of 3232 tickets. Then, after taking a break and having a snack, Candice went on the Ferris wheel 55 times and the roller coaster 22 times, using a total of 2525 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. Equations Setup: Let's denote the number of tickets for one ride on the Ferris wheel as FF and the number of tickets for one ride on the roller coaster as RR. We can then write two equations based on the information given:\newline11) For the first round of rides: 4F+4R=324F + 4R = 32\newline22) For the second round of rides: 5F+2R=255F + 2R = 25
  2. Elimination Method: To solve this system using elimination, we want to eliminate one of the variables. We can do this by multiplying the first equation by a number that will make the coefficient of RR the same in both equations. If we multiply the first equation by 12\frac{1}{2}, we get:\newline(12)(4F+4R)=(12)(32)\left(\frac{1}{2}\right)(4F + 4R) = \left(\frac{1}{2}\right)(32)\newline2F+2R=162F + 2R = 16
  3. New System of Equations: Now we have a new system of equations:\newline11) 2F+2R=162F + 2R = 16\newline22) 5F+2R=255F + 2R = 25\newlineWe can eliminate RR by subtracting the first equation from the second:\newline(5F+2R)−(2F+2R)=25−16(5F + 2R) - (2F + 2R) = 25 - 16\newline3F=93F = 9
  4. Solving for F: Divide both sides of the equation by 33 to solve for F:\newline3F3=93\frac{3F}{3} = \frac{9}{3}\newlineF=3F = 3\newlineSo, it takes 33 tickets to ride the Ferris wheel.
  5. Substitute F into Equation: Now that we know the value of F, we can substitute it back into one of the original equations to find R. Let's use the first equation:\newline4F+4R=324F + 4R = 32\newline4(3)+4R=324(3) + 4R = 32\newline12+4R=3212 + 4R = 32
  6. Solving for R: Subtract 1212 from both sides of the equation to solve for R:\newline12+4R−12=32−1212 + 4R - 12 = 32 - 12\newline4R=204R = 20
  7. Solving for R: Subtract 1212 from both sides of the equation to solve for R:\newline12+4R−12=32−1212 + 4R - 12 = 32 - 12\newline4R=204R = 20Divide both sides of the equation by 44 to solve for R:\newline4R4=204\frac{4R}{4} = \frac{20}{4}\newlineR=5R = 5\newlineSo, it takes 55 tickets to ride the roller coaster.

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