Question

one night a theater sold 548 movie tickets. An adults ticket costs 6.50 and a child's ticket cost 3.50. in all 2881 was taken in. how many of each kind of ticket were sold

Answer 1

`\large \boxed{\text{321 adult tickets and 227 child tickets}}`

Explanation:

1. Set up the equations

Let a = the number of adult tickets

and c = the number of child tickets. Then

6.50a = revenue from adult tickets and

3.50c = revenue from child tickets

6.50a + 3.50c = total ticket revenue

You have a system of two equations:

`\begin{cases}(1) & a + c = 548\\(2) & 9.70a + 5.90c = 2881\end{cases}`

2. Solve the equations

`\begin{array}{lrcll}(4) &a & = & \mathbf{321} &\text{Simplified}\\ &321 + c & = & 548 &\text{Substituted (4) into (1)}\\ &c & = & \mathbf{227} &\text{Subtracted 321 from each side}\\\end{array}\\\text{The museum sold $\large \boxed{\textbf{321 adult tickets and 227 child tickets}}$}`

3. Check

`\begin{array}{rclcrcl}321 + 227& = & 548 & \qquad &6.50(321) + 3.50(227)&=&2881\\548 & = & 548 & \qquad &2086.50 + 794.50& = &2881\\&&& \qquad &2881& = &2881\\\end{array}`

OK.