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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

User David Ford
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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.

User Molavec
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