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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?

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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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Divide numbers ending in zeros: word problems

Full solution

Q. 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

◻

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: $\newline$ $1$ . $C + A = 1,200$ (total tickets) $\newline$ $2$ . $7.50C + 10A = 10,875$ (total sales in dollars) $\newline$ 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: $\newline$ $7.50(1,200 - A) + 10A = 10,875$ $\newline$ 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: $\newline$ $7.50 \times 1,200 - 7.50A + 10A = 10,875$ $\newline$ $9,000 - 7.50A + 10A = 10,875$ $\newline$ Now, we combine like terms: $\newline$ $9,000 + 2.50A = 10,875$
Isolate Term with A: Next, we subtract $9,000$ from both sides to isolate the term with $A$ : $\newline$ $2.50A = 10,875 - 9,000$ $\newline$ $2.50A = 1,875$ $\newline$ Now, we divide both sides by $2.50$ to solve for $A$ : $\newline$ $A = \frac{1,875}{2.50}$
Solve for A: Performing the division gives us the number of adult tickets sold: $A = 750$ So, $750$ adult tickets were sold that evening.

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