Question

A total of 500people attended a concert. Floor ticket costs $20 each while balcony tickets cost $30 each. If a total of $14000 was collected,how many of each ticket was sold

Answer 1

Let the number of floor tickets sold be x.

Let the number of balcony tickets sold be y.

According to the first condition,

$x\text{ + y = 500\_\_\_\_\_\_\lparen1\rparen }$

The total amount collected is $ 14000.

According to the second condition,

$20x\text{ + 30y = 14000\_\_\_\_\_\_\_\lparen2\rparen}$

Multiplying equation (1) by 20,

$20x\text{ + 20y = 10000\_\_\_\_\_\lparen3\rparen}$

Subtracting equation (3) from (2),

$\begin{gathered} 10y\text{ = 4000} \\ y\text{ = 400} \end{gathered}$

Substituting x = 400 in equation (1),

$\begin{gathered} x\text{ + y = 500} \\ 400\text{ + y = 500} \\ x\text{ = 100} \end{gathered}$

Thus a number of floor tickets sold is 100 and the number of balcony tickets sold is 400.