The admission for a school play is $3.50 for children and $9.00 for adults. on a certain day, 312 people attended the play, and the total money collected from sales was $1884. How many children and how many adults were admitted?
C = # children
A = # adults
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A + C = 312
9.00A + 3.50C = 1884
Solve these two equations simultaneously for A and C.
Post your work if you get stuck.
To find out how many children and how many adults were admitted to the school play, we can set up a system of equations.
Let's assume that x represents the number of children and y represents the number of adults attending the play.
From the given information, we can create two equations:
Equation 1: x + y = 312 (Total number of people attending the play)
Equation 2: 3.50x + 9.00y = 1884 (Total money collected from ticket sales)
To solve this system of equations, we can use the substitution method or the elimination method.
Let's use the elimination method:
Multiply Equation 1 by 3.50 to make the coefficients of x in both equations equal:
3.50(x + y) = 3.50(312)
3.50x + 3.50y = 1092 (Equation 3)
Subtract Equation 3 from Equation 2:
(3.50x + 9.00y) - (3.50x + 3.50y) = 1884 - 1092
5.50y = 792
Divide both sides of the equation by 5.50:
y = 792 / 5.50
y ≈ 144
Now, substitute the value of y back into Equation 1:
x + 144 = 312
x = 312 - 144
x ≈ 168
Therefore, approximately 168 children and 144 adults were admitted to the school play.