For one performance of a play, 416 tickets were sold. Reserved seat tickets sold for $14 each, and general admission tickets sold for $8 each. Receipts from the sale of the tickets totaled $4840. Find the number of general admission tickets sold.
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To find the number of general admission tickets sold, we can set up a system of equations based on the given information.
Let's assume the number of reserved seat tickets sold is represented by R, and the number of general admission tickets sold is represented by G.
From the problem, we know that the total number of tickets sold is 416, so we can write the equation:
R + G = 416 (Equation 1)
We also know that the total receipts from ticket sales is $4840, so we can write the equation:
14R + 8G = 4840 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:
From Equation 1, we have R = 416 - G. We can substitute this value of R in Equation 2:
14(416 - G) + 8G = 4840
Distributing, we get:
5824 - 14G + 8G = 4840
Combining like terms, we have:
-6G + 5824 = 4840
Subtracting 5824 from both sides of the equation, we get:
-6G = 4840 - 5824
-6G = -984
Dividing both sides by -6, we find:
G = -984 / -6
G = 164
Therefore, the number of general admission tickets sold is 164.