Question

Which system of equations could be used to find the number of tickets sold before the tournament, x, and the number of tickets sold at the door, y? Remember, 743 tickets were sold, and 75 more tickets were purchased before the tournament than at the door.

Select the correct system based on the scenario.
y = x + 75
y = 75x + 743
y = x + 75
y = x + 743
x + y = 743
x – y = 75
x + y = 743
y – x = 75

Answer 1

To represent the scenario where 743 tickets were sold in total, and 75 more tickets were purchased before the tournament than at the door, we need to formulate a system of equations based on these two pieces of information.

1. The first piece of information states that 743 tickets were sold in total, which can be represented by the equation:

\[ x + y = 743 \]
where \( x \) is the number of tickets sold before the tournament and \( y \) is the number of tickets sold at the door.

2. The second piece of information states that there were 75 more tickets sold before the tournament than at the door, which can be represented by:

\[ x = y + 75 \]
or equivalently,
\[ y = x - 75 \]

Considering the options available, the correct system would be:

\[ x + y = 743 \]
\[ x - y = 75 \]

So the correct answer is:

**x + y = 743**
**x - y = 75**