Answer:
Step-by-step explanation:
The given relations between numbers and prices can be used to write a system of equations for the number of each kind of ticket. One equation will describe ticket numbers; the other will describe ticket revenue.
<h3>Setup</h3>
Let x represent the number of adult tickets, and y the number of student tickets. The given relations can be written as the general-form equations ...
8x -y -11 = 0 . . . . . . . . . ticket numbers
5x +3y -895 = 0 . . . . . ticket revenue
<h3>Solution</h3>
The setup using general form equations lends itself to solution using the "cross multiplication method." Using this method, we define three numbers used in the solution:
Δ = 8(3) -5(-1) = 24 +5 = 29
Δx = -1(-895) -3(-11) = 895 +33 = 928
Δy = -11(5) -(-895)(8) = -55 +7160 = 7105
And the solutions are ...
x = Δx/Δ = 928/29 = 32
y = Δy/Δ = 7105/29 = 245
32 adult tickets and 245 student tickets were sold.
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For more about the Cross Multiplication Method, see ...
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