SOLUTION: Six hundred people attended the premiere of a motion picture. Adult tickets cost $8, and children were admitted for $6. If box office receipts totaled $4400, how many children atte

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Question 1192865: Six hundred people attended the premiere of a motion picture. Adult tickets cost $8, and children were admitted for $6. If box office receipts totaled $4400, how many children attended the premiere?
Answer by greenestamps(13198) About Me  (Show Source):
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A standard formal algebraic setup for solving the problem....

x = # of adult tickets
600-x = # of child tickets

The total cost of the tickets was $4400:

8%28x%29%2B6%28600-x%29=4400

That equation is easily solved using basic algebra:

8x%2B3600-6x=4400
2x=800
x=400

x=400 adult tickets; so 600-x=200 children tickets.

ANSWER: 200 child tickets

If formal algebra is not required, here is a quick solution method using logical reasoning and simple mental arithmetic.

600 adult tickets would have cost $4800; 600 child tickets would have cost $3600.
The actual total, $4400, is 2/3 of the way from $3600 to $4800; therefore, 2/3 of the tickets were adult tickets.

So 2/3 of 600 = 400 adult tickets, and 1/3 of 600 = 200 child tickets.