Question

tickets for a celebrity golf tournament were sold before the tournament and on the day of the tournament. after reviewing ticket sales, the tournament director found that 150 fewer tickets were purchased on the day of the tournament than before the tournament. a total of 898 tickets were sold. how many tickets were sold on the day of the tournament?

314 tickets
374 tickets
524 tickets
748 tickets

Explanation:

Define variables for ticket sales

Using the Variable Identification knowledge point, we define:

• Let \(x\) be the number of tickets sold before the tournament.
• Let \(y\) be the number of tickets sold on the day of the tournament.

Translate the relationships into equations

Using the Algebraic Translation knowledge point:

• The total number of tickets sold is 898:

$$x + y = 898$$

• There were 150 fewer tickets sold on the day of the tournament than before:

$$y = x - 150$$

Solve the system of equations

Using the System of Equations knowledge point, we substitute \(y = x - 150\) into the first equation:

$$x + (x - 150) = 898$$

$$2x - 150 = 898$$

$$2x = 1048$$

$$x = 524$$

Calculate the target value

We find the tickets sold on the day of the tournament, \(y\):

$$y = 524 - 150$$

$$y = 374$$

Answer:

• 314 tickets
• 374 tickets (Correct answer)
• 524 tickets
• 748 tickets