A theatre charges $25 for adults and $15 for children. All 200 seats in the theatre were sold on opening night and the ticket sales totalled $4350.Calculate the number of adult tickets sold.
Question
A theatre charges 15 for children. All 200 seats in the theatre were sold on opening night and the ticket sales totalled $4350.Calculate the number of adult tickets sold.
Solution
Let's denote the number of adult tickets sold as A and the number of children tickets sold as C.
We know two things from the problem:
-
A + C = 200 (because all 200 seats were sold)
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25A + 15C = 4350 (because the total sales were $4350)
We can solve this system of equations step by step:
Step 1: Multiply the first equation by 15 to make the coefficients of C the same in both equations:
15A + 15C = 3000
25A + 15C = 4350
Step 2: Subtract the first equation from the second to eliminate C:
25A - 15A = 4350 - 3000
10A = 1350
Step 3: Divide by 10 to solve for A:
A = 1350 / 10 = 135
So, 135 adult tickets were sold.
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