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Question: At the movie theatre, child admission is $5.20 and adult admission is $9.90. On Saturday, 149 tickets were sold for a total sales of $1,075.60. How many child tickets were sold that day?
Let's denote the number of child and adult tickets as C and A respectively. We'll start with the information given: C tickets for children are sold for $5.20 each, while A tickets for adults are sold for $9.90 each. Together they've sold 149 tickets for $1075.60. This gives us the following two equations: 1) C + A = 149 (equation for the total number of tickets) 2) 5.20C + 9.90A = 1075.60 (equation for the total cost) We have a system of two equations with two variables (C and A). Let's solve that. To eliminate one of the variables, we can multiply the first equation by 5.20, which gives: 5.20C + 5.20A = 773.80 Then, subtract the new equation from the second one: 5.20C + 9.90A - (5.20C + 5.20A) = 1075.60 - 773.80 4.70A = 301.80 To find the number of adult tickets, divide both sides of the equation by 4.70: A = 301.80 / 4.70 ≈ 64.21 Since the number of tickets sold has to be a whole number, we'll round the number of adult tickets to 64. Then substitute A = 64 to find C: C + 64 = 149 C= 149 - 64 = 85 So, approximately 85 child tickets and 64 adult tickets were sold that day.
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