sarah is spending the day at a state fair while at the fair she can play games or ride rides when sarah arrives at the fair she purchases 26 tickets and wants to use all of the tickets that she purchases. playing a game at the fair requires four tickets and riding a ride at a the fair requires six tickets. to make her trip to the fair worthwhile sarah decides she must participate in seven activities at the fair. create a system of equation to model the situation above and use it to determine if the solution of the system is viable

Question

sarah is spending the day at a state fair while at the fair she can play games or ride rides when sarah arrives at the fair she purchases 26 tickets and wants to use all of the tickets that she purchases. playing a game at the fair requires four tickets and riding a ride at a the fair requires six tickets. to make her trip to the fair worthwhile sarah decides she must participate in seven activities at the fair. create a system of equation to model the situation above and use it to determine if the solution of the system is viable

Answer 1

Let:

x = number of games Sarah plays
y = number of rides Sarah goes on

We can create the following system of equations:

4x + 6y = 26 (Sarah purchases 26 tickets)
x + y = 7 (Sarah participates in seven activities)

Now, let's solve the system:

x + y = 7
x = 7 - y

Substitute x = 7 - y into the first equation:

4(7 - y) + 6y = 26
28 - 4y + 6y = 26
2y = -2
y = -1

Since we cannot have a negative number of rides, the solution is not viable. This means that Sarah cannot use all 26 tickets and participate in seven activities based on the given conditions.