SOLUTION: Adult tickets for a play cost $25 each and children'ts tickets cost $15 each. The total receipts were $7200 and the total attendance ws 400. How many adults and how many children a

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Question 189537: Adult tickets for a play cost $25 each and children'ts tickets cost $15 each. The total receipts were $7200 and the total attendance ws 400. How many adults and how many children attended?
Answer by feliz1965(151) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = adult tickets
Let c = children tickets
Then a + c = 400....This is one equation.
The second equation is 25a + 15c = 7200.
We have a system of linear equations in two variables.
a + c = 400
25a + 15c = 7200
Can you solve it now?
I suggest using the substitution method which far easier than any other method.
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I got your reply.
Let a = adult tickets
Let c = children tickets
Then a + c = 400....This is one equation.
The second equation is 25a + 15c = 7200.
We have a system of linear equations in two variables.

a + c = 400...Equation A
25a + 15c = 7200

I will solve for a in Equation A.

a = 400 - c

I will now plug 400 - c into Equation B for a.

25(400 - c) + 15c = 7200

10000 - 25c + 15c = 7200

-10c = 7200 - 10000

-10c = -2800

c = -2800/-10

c = 280 tickets

The number of children tickets is 280.

To find the number of adult tickets, we plug 280 for c into EITHER Equation A or Equation B (your choice).

I will use Equation A.

a + c = 400

a + 280 = 400

a = 400 - 280

a = 120

The number of adult tickets is 120.

Understand?
NOTE: The number of children tickets cannot be 250. The correct answer is 280.
HERE IS THE PROVE:
adult tickets = 120 x $25 each = $3000
children tickets = 280 x $15 each = $4200
Together = $3000 + $4200 = $7200