Question

The attendance at a football game was 400 people. Lower deck seats sold for $15 and upper deck seats sold for $10. Total ticket sales were $4650. How many of each type of ticket were sold?

Answer 1

We have the next variables

x--- people in the lower deck

y-- people in the upper deck

the first equation is

x+y=400

this equation is the number of people that go to the game

The second equation is

x(15)+y(10)=4650

15x+10y=4650

this equation represents the total sales

In order to solve the system of equation, we will isolate the x of the first equation

x=400-y

then this equation will substitute in the second equation

15(400-y)+10y=4650

6000-15y+10y=4650

then we sum similar terms

5y=4650-6000

5y=1350

y=1350/5

y=270

then we substitute the value of y in the equation with the x isolate

x=400-y

x=400-270

x=130

the solution is

130 lower deck seats were sold

270 upper deck seats were sold