Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Isaac loves riding Ferris wheels and roller coasters. While visiting the Washington County Fair, he first went on the Ferris wheel 1 time and the roller coaster 2 times, using a total of 15 tickets. Then, after taking a break and having a snack, Isaac went on the Ferris wheel 3 times and the roller coaster 3 times, using a total of 27 tickets. How many tickets does it take to ride each attraction?It takes tickets to ride the Ferris wheel, and tickets to ride the roller coaster.
Question
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Isaac loves riding Ferris wheels and roller coasters. While visiting the Washington County Fair, he first went on the Ferris wheel 1 time and the roller coaster 2 times, using a total of 15 tickets. Then, after taking a break and having a snack, Isaac went on the Ferris wheel 3 times and the roller coaster 3 times, using a total of 27 tickets. How many tickets does it take to ride each attraction?It takes tickets to ride the Ferris wheel, and tickets to ride the roller coaster.
Solution
Let's denote the number of tickets for the Ferris wheel as F and for the roller coaster as R.
From the problem, we can write two equations:
1F + 2R = 15 (Isaac went on the Ferris wheel 1 time and the roller coaster 2 times, using a total of 15 tickets)
3F + 3R = 27 (Isaac went on the Ferris wheel 3 times and the roller coaster 3 times, using a total of 27 tickets)
We can simplify the second equation by dividing by 3:
F + R = 9
Now we have a system of two equations:
1F + 2R = 15 F + R = 9
We can solve this system by elimination. Subtract the second equation from the first to eliminate F:
1F + 2R - (F + R) = 15 - 9 R = 6
Substitute R = 6 into the second equation:
F + 6 = 9 F = 3
So, it takes 3 tickets to ride the Ferris wheel, and 6 tickets to ride the roller coaster.
Similar Questions
Erin wants to ride the Ferris wheel, the roller coaster, and the log ride. The Ferris wheel costs 6 tickets, the roller coaster costs 3 tickets and the log ride costs 7 tickets. Erin has 8 tickets. How many more tickets should Erin buy?
Tammy wants to ride the bumper cars 5 times and the Ferris wheel 4 times. It costs 4 tickets to ride the bumper cars and 3 tickets to ride the Ferris wheel. How many tickets does Tammy need?
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a system of equations that could be used to determine the number of games Nolan played and the number of rides Nolan went on. Define the variables that you use to write the system.
Ralph spent $132 to buy movie tickets for 20 students and 4 adult chaperones. Adult tickets cost $3 more than student tickets. If A𝐴 is the price of an adult ticket and S𝑆 is the price of a student ticket, which system of equations could be used to find the price of each adult and student ticket? {A+S=320A+4S=132{𝐴+𝑆=320𝐴+4𝑆=132 {A=S+3A+S=132{𝐴=𝑆+3𝐴+𝑆=132 {S=A+34A+20S=132{𝑆=𝐴+34𝐴+20𝑆=132 {A=S+34A+20S=132{𝐴=𝑆+34𝐴+20𝑆=132
A group of friends wants to go to the amusement park. They have $86 to spend on parking and admission. Parking is $5, and tickets cost $13.50 per person, including tax. Write and solve an equation which can be used to determine xx, the number of people who can go to the amusement park.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.