If the school sold twice as many main floor seats as balcony seats and made $870, hoe many of each type of seat did they sell?

Question

Madison High School is putting on a school play. They decide to charge $11 for main floor seats and $7 for balcony seats. If the school sold twice as many main floor seats as balcony seats and made $870, hoe many of each type of seat did they sell?

Answer 1

Let m be the number of main floor seats sold and b be the number of balcony seats sold.

 

870 = 11m + 7b

m = 2b

 

870 = 11(2b) + 7b = 22b + 7b = 29b

b = 30

m = 60

 

They sold 60 main floor seats and 30 balcony seats.

Answer 2

Figure out what you have and what you need, then set up the equation.

You have 870 dollars total for all seats sold:

You have main floor seats sold at 11 dollars a piece.

You have balcony seats sold at 7 dollars a piece.

Now you need to know how many of each were sold.

You have 2 times as many floor seats sold than balcony seats, so we say:

 

Let x = balcony seats sold

Let 2x = floor seats sold

 

Set up the equation:

 

x(7) + 2x(11) = 870

7x + 22x = 870

29x = 870

x = 30 ; This is the amount of balcony seats:

2x = 60 ; This is the amount of floor seats: