Question

Tickets for a drumline competition cost $5 at the gate and $3 in advance. One hundred more tickets were sold in advance than at the gate. The total revenue from ticket sales was $1990. How many tickets were sold in advance?

Answer 1

Answer:

The number of tickets sold at the gate is $G = 211.25$

The number of tickets sold in advance is  $A = 311.25$

Step-by-step explanation:

From the question we are told that

 The cost of a tickets at the gate is $a = \ 5$  

  The cost of a ticket in advance is  $b = \ 3$

Let the number of ticket sold in the gate be G

Let the number of ticket sold in advance  be   A

From the question we are told that

  One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as

       $G + 100 = A$

From the question we are told that

  The total revenue from ticket sales was $1990  and this can be mathematically represented as

    $5 G + 3A = 1990$

substituting for  A in the equation above

    $5 G + 3[G + 100]= 1990$    

    $5 G + 3G + 300= 1990$    

    $8G + 300= 1990$  

    $8G = 1690$

=>  $G = 211.25$

Substituting this for G in the above equation

     $5 [211.25] + 3A = 1990$

=>    $3A = 1990 - 1056.25$

=>    $A = 311.25$