SOLUTION: Tickets for a play at the community theater cost $12 for an adult and $4 for a child. If 130 tickets were sold and the total receipts were $840, how many of each type of ticket we

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Question 102892: Tickets for a play at the community theater cost $12 for an adult and $4 for a child. If 130 tickets were sold and the total receipts were $840, how many of each type of ticket were sold?
Answer by doukungfoo(195) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the number of adult tickets sold
let y equal the number of child tickets sold
we are told that there were a total of 130 tickets sold so
x + y = 130
we are also told that adult tickets cost $12 and child tickets cost $4
and the total receipts were $840 so this means that
12x + 4y = 840
In other words $12 times the number of adult tickets sold plus $4 times the number of child tickets sold equals $840
Ok so now we have a system of equations that we can use to solve for x and y
I will demonstrate how to solve the system by using the substitution method.
Lets take the first equation and set it equal to x
x + y = 130
To do this subtract y from both sides of the equal sign
x + y - y = 130 - y
The y's on the left side cancel out and we are left with
x = 130 - y
now take the second equation and substitute x with 130-y and solve for y
12x + 4y = 840
12(130-y) + 4y = 840
multiply 12 across (130-y)
1560 - 12y + 4y = 840
combine like terms
1560 - 8y = 840
subtract 1560 from both sides
1560 - 1560 - 8y = 840 - 1560
0 - 8y = -720
-8y = -720
divide both sides by -8
-8y/-8 = -720/-8
y = 90
Answer: The theater sold 90 child tickets
Now use this to find out how many adult tickets were sold
x + y = 130
x + 90 = 130
x = 130 - 90
x = 40
Answer: The theater sold 40 adult tickets
Check both answers in both equations
x + y = 130
40 + 90 = 130
130 = 130
AND
12x + 4y = 840
12(40) + 4(90) = 840
480 + 360 = 840
840 = 840