Question 822610: Solve by setting up a system of linear equations with 2 variables and 2 unknowns. An overwhelmed concert manager realized the next day after a concert that 350 ticket receipts were counted. The price for a student ticket was $12.50 and the price for an adult ticket was $16.00. The register confirmed $5,075 was taken in, too. What the manager did not keep track of was the number of student tickets and the number of adult tickets that were sold. How many of each were sold?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let a = no. of adult tickets
let s = no. of student tickets
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Write an equation for each statement
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the next day after a concert that 350 ticket receipts were counted.
a + s = 350
s = (350-a); use this form for substitution
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The price for a student ticket was $12.50 and the price for an adult ticket was $16.00.
The register confirmed $5,075 was taken in, too.
16a + 12.50s = $5075
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How many of each were sold
Replace s with (350-a)
16a + 12.5(350-a) = $5075
16a + 4375 - 12.5a = 5075
16a - 12.5a = 5075 - 4375
3.5a = 700
a = 700/3.5
a = 200 adults
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I'll let you find the number of students, check solutions in $$ equations
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