Question 67483: This is one of my problems that hopefully yall can help me on, "Tickets for a football game cost $1.00 each if purchased before the day of the game. They cost $1.50 each if bought at the gate. For the homecoming game, 600 tickets were sold, with receipts of $700. How many tickets were sold at the gate?" Can yall help me please?
Found 2 solutions by ankor@dixie-net.com, bam878s:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Tickets for a football game cost $1.00 each if purchased before the day of the game. They cost $1.50 each if bought at the gate. For the homecoming game, 600 tickets were sold, with receipts of $700. How many tickets were sold at the gate?"
:
Let x = number of gate tickets, ($1.50)
:
Since there were 600 tickets sold, let (600-x) = the $1 tickets
:
1.50 tickets + $1 tickets = $700
:
1.5x + 1(600 - x) = 700
1.5x - x = 700 - 600
.5x = 100
x = 100/.5
x = 200 ea 1.50 tickets sold at the gate
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Check: there were 600 - 200 = 400 ea $1 tickets sold
1.50(200) + 1(400) = $700
Answer by bam878s(77)  (Show Source):
You can put this solution on YOUR website! Let x = number of tickets sold before the game and y = the number of tickets sold the day of the game. Now from the information provided, we know that tickets purchased before the day of the game cost $1.00 and those purchased the day of the game cost $1.50. Also $700 was sold from 600 in sales of tickets. From this information, we have:
x + y = 600, and
$1.00(x) + $1.50(y) = $700.
From the first of these equations we can solve for x
x + y = 600 ==> x = 600 - y (subtracting y from both sides)
Now, since we know x, we can plug this into the second equation above
$1.00(x) + $1.50(y) = $700 ==> $1.00(600-y) + $1.50(y) = $700
Now multiply the $1.00 into the 600 - y as follows:
$1.00(600-y) + $1.50(y) = $700 ==> 600 - y + 1.50y = $700
==> 600 + 0.5y = 700. So now we can solve for y which is the number of tickets sold at the gate!
600 + 0.5y = 700 (subtract 600 from both sides)
0.5y = 100 (now divde both sides by 0.5)
y = 200
So, there were 200 tickets sold at the gate. You could also figure out how many were sold before the game day by plugging this value of y into one of the original equations and solving for x, but this is not required in the question. Only need to solve for y (the number of tickets sold at the gate)
Hope this helps!!
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