An equation that represents the total revenue is 5x + 4y = 2674.
An equation that represents the total number of tickets sold is 1/7(x) + 4/7(y) = 262.
The number of seats in each section are 210 lower level seats and 406 upper level seats.
In order to write a system of linear equations to describe this situation, we would assign variables to the total number of seats, and then translate the word problem into a linear equation as follows:
- Let the variable x represent the total number of lower level seats.
- Let the variable y represent the total number of upper level seats.
Since seats sells for $5 each in the lower level and $4 each in the upper level, and the total revenue is $2,674, a linear equation that models the total revenue is given by;
5x + 4y = 2674
Additionally, an equation that represents the total number of tickets sold is;
1/7(x) + 4/7(y) = 262
1/7(x) × 7 + 4/7(y) × 7 = 262 × 7
x + 4y = 1834
By solving the system of equations simultaneously using the elimination method, we have;
5x + 4y = 2674
x + 4y = 1834
4x = 840
x = 840/4
x = 210 lower level seats.
For the value of y, we have;
y = (1834 - x)/4
y = (1834 - 210)/4
y = 406 upper level seats.
Missing information:
Seats at a local entertainment venue sell for $5 each in the lower level and $4 each in the upper level. If all the seats are sold, the total revenue is $2,674. At a recent event, only 1/7 of the lower level seats and 4/7 of the upper level seats were sold, for a total of 262 seats.
Let x represent the total number of lower level seats, and let y represent the total number of upper level seats.
Which equation represents the total revenue?
Which equation represents the total number of tickets sold?
How many seats does each section have?