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.
Find the equation of the line that contains the point (0, 4) and is parallel to the line 3x – 4y = 8.
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If there were g general tickets, then the rest (416-g) were reserved.
Now add up all the receipts:
8g+14(416-g) = 4840
Now just solve for g.
3x-4y=8 has slope 3/4
So, you want the line through (0,4) with slope 3/4:
y-4 = 3/4 (x-0)
Or, you can think of it like this:
all lines of the form
3x – 4y = C
are parallel to the line 3x – 4y = 8
So, plug in your point (0,4) and you have
3(0)-4(4) = -16
So, your new line is
3x – 4y = -16
which is the same line derived above with the point-slope form.
To find the number of general admission tickets sold, let's set up a system of equations based on the given information:
Let's say that the number of reserved seat tickets sold is represented by R, and the number of general admission tickets sold is represented by G.
We know that a total of 416 tickets were sold, so we can write the equation:
R + G = 416 ...(1)
We also know that the receipts from the sale of the tickets totaled $4840. Since reserved seat tickets sold for $14 each and general admission tickets sold for $8 each, we can write the equation:
14R + 8G = 4840 ...(2)
Now, we have a system of equations with two unknowns (R and G). We can solve this system to find the values.
Let's solve the given system of equations:
Equation (1) can be rewritten as:
R = 416 - G
Substituting this value of R into equation (2), we get:
14(416 - G) + 8G = 4840
Expanding the equation:
5824 - 14G + 8G = 4840
Combine like terms:
-6G = 4840 - 5824
-6G = -984
Divide both sides by -6:
G = -984 / -6
G = 164
Thus, the number of general admission tickets sold is 164.