SOLUTION: a concert results in $11,200 in revenue from selling 400 tickets. a regular ticket costs $30, and the student discounted ticket costs $25. how many people purchased tickets at the
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-> SOLUTION: a concert results in $11,200 in revenue from selling 400 tickets. a regular ticket costs $30, and the student discounted ticket costs $25. how many people purchased tickets at the
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Question 1199241: a concert results in $11,200 in revenue from selling 400 tickets. a regular ticket costs $30, and the student discounted ticket costs $25. how many people purchased tickets at the regular price? Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! x = the number of regular tickets.
y = the number of discounted tickets.
your equations are:
x + y = 400
30x + 25y = 11200
these two equations need to be solved simultaneously.
multiply both sides of the first equation by 30 and leave the second equation as is to get:
30x + 30y = 12000
30x + 25y = 11200
subtract the second equation from the first to get:
5y = 800
solve for y to get:
y = 800/5 = 160
since x + y = 400, then x = 240
your solution is that 240 adult tickets were sold and 160 discount tickets were sold.
x + y = 400 becomes 240 + 160 = 400 which is true.
30x + 25y = 11200 becomes 30 * 240 + 25 * 160 = 11200 which is true.
solution is confirmed to be good.
required solution is that 240 tickets were purchased at the regular price.
Here is an informal solution method, using logical reasoning and mental arithmetic instead of formal algebra.
If all 400 tickets had been student discounted tickets, the total revenue would have been 400($25) = $10,000.
The actual total revenue was $11,200, which is $1200 more.
The difference in cost between the two kinds of tickets is $5; the number of regular price tickets needed to make up the additional $1200 is 1200/5 = 240.
