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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 25foradultsand25 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.

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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:

  1. A + C = 200 (because all 200 seats were sold)

  2. 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.

This problem has been solved

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