SOLUTION: PROBLEM: Kevin and Ansu were in charge of the box office for the school play last night. Theyknow that they sold a total of 198 tickets, and that they made a total of $878.00. The

Algebra ->  College  -> Linear Algebra -> SOLUTION: PROBLEM: Kevin and Ansu were in charge of the box office for the school play last night. Theyknow that they sold a total of 198 tickets, and that they made a total of $878.00. The      Log On


   

Question 173822: PROBLEM:
Kevin and Ansu were in charge of the box office for the school play last night. Theyknow that they sold a total of 198 tickets, and that they made a total of $878.00. They also know that adult tickets sold for $5.00 each, and that student tickets sold for $3.00 each. The problem is, they can’t remember how many of each type of ticket they sold.Use the information provided to determine how many adult tickets and how manystudent tickets they sold.
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
let a = number of adult tickets sold.
let s = number of student tickets sold.
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a + s = 198 since the total number of tickets sold is 198.
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5*a + 3*s = 878 since the total amount of money made is 878 dollars and each adult ticket brought in 5 dollars and each student ticket brought in 3 dollars.
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you have 2 equations that need to be solved simultaneously. this means the same value for a and the same value for s applies to both equations.
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the 2 equations are:
a + s = 198
5*a + 3*s = 878
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to solve by substitution, take one of the equations and solve for one variable in terms of the other.
take a+s = 198 and solve for a.
a+s = 198
subtract s from both sides:
a = 198 - s
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substitute 198-s for a in the second equation:
5*a + 3*s = 878
5*(198-s) + 3*s = 878
990 -5*s + 3*s = 878
combine like terms:
990 - 2*s = 878
subtract 878 and add 2*s to both sides of the equation:
990 - 878 = 2*s
combine like terms:
112 = 2*s
divide both sides by 2:
56 = s
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you have s = 56.
take your first equation and solve for a.
a + s = 198
a + 56 = 198
a = 198-56
a = 142
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you have:
a = 142
s = 56
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takes these numbers and plug into your second equation:
5*a + 3*s = 878
5*142 + 3*56 = 878
710 + 168 = 878
878 = 878
equation is true.
values for a and s are good.
your answer is:
142 adult tickets were sold and 56 student tickets were sold.