There was a toatl of 2612 tickets sold for $41,320 to a concert. Floor seats cost $20 and balcony seats cost $10. How many of each type of seat was sold?

Question

Need to find how many of each ticket was told either being twenty dollars or ten dollars for the ticket.

Answer 1

These type problems are easily solved by writing two equations and then solving by substitution.

 

Step 1 determine what your variables are going to represent:

    

    F = # of floor seats sold

    B = # of balcony seats sold

 

Step 2   write two equations: one representing tickets and one representing money

 

   Equation 1      F + B = 2612 (total tickets sold)

 

   Equation 2      $20F + $10B = $41320 (total money raised)

 

Step 3    solve the first equation for either F or B and then substitute it into the second equation

 

Step 4    take the value you found in step three and plug it into equation 1 to find the other value.

 

*Once you have found your answers, post them and I will be happy to check it for you.

 

 

 

Answer 2

Krystle,

 

If we let N₁=number of floor seats sold and N₂=number of balcony seats sold then if we translate the give information into equations we have

 

1. N₁+N₂=2612 (total tickets sold)

2.20N₁+10N₂=41,320 (total sales from tickets)

 

All you have to do now is solve 1. for say N₁ in terms of N₂  and substitute  it in 2. and solve for N₁. See if you can do it.

I got N₂=1092 and N₁=1520 if I did the arithmetic correctly

 

Jim