Thomas was selling tickets to his school play. The tickets cost $5.00 for adults and $2.00 for children. He sold 200 tickets and collected $610. Which system represents the number of adult and child tickets that Thomas sold?

Question

x + y = 200. 5 x + 2 y = 610.
x + y = 610. 5 x + 2 y = 200.
x + y = 200. x + 2 y = 610.
x + y = 200. 5 x + y = 610.

Answer 1

To solve this problem, let's define the variables:

• Let \( x \) be the number of adult tickets sold.
• Let \( y \) be the number of child tickets sold.

Given that:

1. The total number of tickets sold is 200: \[ x + y = 200 \]
2. The total amount of money collected is $610, with adult tickets costing $5.00 and children tickets costing $2.00: \[ 5x + 2y = 610 \]

Now, looking at the options provided:

1. \( x + y = 200 \) \quad and \quad \( 5x + 2y = 610 \) is correct.
2. \( x + y = 610 \) \quad and \quad \( 5x + 2y = 200 \) is incorrect.
3. \( x + y = 200 \) \quad and \quad \( x + 2y = 610 \) is incorrect.
4. \( x + y = 200 \) \quad and \quad \( 5x + y = 610 \) is incorrect.

Thus, the correct system that represents the number of adult and child tickets that Thomas sold is:

\[ \begin{aligned} x + y &= 200 \ 5x + 2y &= 610 \end{aligned} \]

So the answer is the first option.