Respuesta :
Answer:
The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.
Step-by-step explanation:
Let x represent the number of seats in the lower section then the number of seats in the upper section is 3x and y the number of seats in the field.
The equation can be written as
80x + 60 (3x) + 40 y= $1,140,000-----1
And x+ 3x+ y= 24,200------2
4x+ y= 24,200
or y= 24,200-4x----3
Solving Eq 1
80x + 180x + 40 y= $1,140,000
260x+ 40 y=$1,140,000-----4
Putting Eq 3 in Eq 4
260x+ 40 y=$1,140,000
260x+ 40(24,200-4x-)=$1,140,000
260x + 968,000- 160x= $1,140,000
100x= $1,140,000-968,000
100x= 172,000
x= 1720
The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.
Putting the values of x and y in Eq 1 we get the same revenue.
80x + 60 (3x) + 40 y= $1,140,000
80(1720) + 60 (5160) + 40( 17320)= $1,140,000
137600 + 309600 + 692800= $1,140,000
137600 + 1002400= $1,140,000
The total number of seats in the upper section is 5160, in the lower section is 1720 and the total number of seats in the field is 17320.
Given :
- A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets.
- There are three times the amount of seats in the upper section as the lower section.
- The revenue from selling all 24,200 tickets is $1,140,000.
The following steps can be used in order to determine the total number of seats in each section:
Step 1 - In the lower section let the total number of seats be 'x'. So according to the given data, in the upper field, the total number of seats is '3x'. Now, let the total number of seats in the field be 'y'.
Step 2 - The linear equation that represents total revenue from the tickets.
[tex]\rm 80x + 60(3x)+40y = 1140000[/tex]
260x + 40y = 1140000 --- (1)
Step 3 - The linear equation that represents the total number of tickets is:
x + 3x + y = 24200
y = 24200 - 4x --- (2)
Step 4 - Substitute the value of y in equation (1).
260x + 40(24200 - 4x) = 1140000
x = 1720 tickets
Step 5 - Substitute the value of 'x' in equation (2).
y = 24200 - 4(1720)
y = 17320 tickets
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https://brainly.com/question/11897796
