Set up and solve a system of equations
The school that Joe goes to is selling tickets to a spring musical. On the first day of ticket sales the school sold 12 adult tickets and 2 child for a total of $122. The school took $160 on the second day by selling 7 adult tickets and 8 child tickets. What is the price each of one adult ticket and one child ticket?
To solve this problem, we need to set up a system of equations using the given information.
Let's assume that the price of an adult ticket is $x, and the price of a child ticket is $y.
According to the given information, on the first day of ticket sales, the school sold 12 adult tickets and 2 child tickets for a total of $122. This can be described by the equation:
12x + 2y = 122
On the second day, the school sold 7 adult tickets and 8 child tickets for a total of $160, which can be represented by the equation:
7x + 8y = 160
Now that we have the system of equations, we can solve for the values of x and y.
One way to solve this system is to use the method of substitution.
Start by solving one equation for one variable and substituting it into the other equation. Let's solve the first equation for x:
12x = 122 - 2y
x = (122 - 2y) / 12
Now substitute this value of x into the second equation:
7((122 - 2y) / 12) + 8y = 160
Simplify this equation and solve for y:
854 - 14y + 96y = 1920
Combine like terms:
82y = 1066
Divide both sides by 82:
y = 13
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x:
12x + 2(13) = 122
12x + 26 = 122
12x = 122 - 26
12x = 96
x = 8
Therefore, the price of one adult ticket is $8, and the price of one child ticket is $13.
12a+2c = 122
7a+8c = 160
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