At Charlie's Cinema, a total of 1,200 adult and child movie tickets were sold to bring in $10,875 in ticket sales one evening. If each child ticket costs $7.50 and each adult ticket costs $10.00, how many adult tickets were sold that evening? ◻

Question

At Charlie's Cinema, a total of 1,200 adult and child movie tickets were sold to bring in $10,875 in ticket sales one evening. If each child ticket costs $7.50 and each adult ticket costs $10.00, how many adult tickets were sold that evening?  ◻

Bytelearn · Accepted Answer

Denote Tickets and Sales: Let's denote the number of child tickets sold as C and the number of adult tickets sold as A. We are given two equations based on the total number of tickets and the total sales: 1. C + A = 1,200 (total tickets) 2. 7.50C + 10A = 10,875 (total sales in dollars) We need to solve this system of equations to find the value of A, the number of adult tickets sold.Rearrange First Equation: First, we can rearrange the first equation to express C in terms of A: C = 1,200 - A This will allow us to substitute the value of C in the second equation.Substitute C in Second Equation: Now, let's substitute C = 1,200 - A into the second equation: 7.50(1,200 - A) + 10A = 10,875 This will give us an equation with one variable, A, which we can solve for.Distribute and Simplify: Let's distribute 7.50 into the parentheses and simplify the equation: 7.50 * 1,200 - 7.50A + 10A = 10,875 9,000 - 7.50A + 10A = 10,875 Now, we combine like terms: 9,000 + 2.50A = 10,875Isolate Term with A: Next, we subtract 9,000 from both sides to isolate the term with A: 2.50A = 10,875 - 9,000 2.50A = 1,875 Now, we divide both sides by 2.50 to solve for A: A = 1,875 / 2.50Solve for A: Performing the division gives us the number of adult tickets sold: A = 750 So, 750 adult tickets were sold that evening.

At Charlie's Cinema, a total of $1,200$ adult and child movie tickets were sold to bring in $\$10,875$ in ticket sales one evening. If each child ticket costs $\$7.50$ and each adult ticket costs $\$10.00$ , how many adult tickets were sold that evening? $\newline$ ◻

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