Question 173822
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.