Answer:
Section A has 27,500 seats
Section B has 14,800 seats
Section C has 12,700 seats
Step-by-step explanation:
To solve this, we will have equations:
let x = seats at section A
y= seats at section B
Z = seats at section C
we will get the following equation:
So from the question, x = y + z ..........(1)
x + y + z = 55,000 .........(2)
42x + 24y + 18z = 1,738,800 .... (3)
input equation (1) into (2)
y + z + y + z = 55,000
2y + 2z = 55,000...... (4)
so for exuation (3), input equation (1) into (3):
42x + 24y + 18z = 1,738,800
42(y + z) + 24y + 18z = 1,738,800
42y + 42z + 24y + 18z = 1,738,800
collect like terms:
66y + 60z = 1,738,800 ..... (5)
multiply equation (4) by -30. -30 is chosen to remove z from the equation so we could get what y is
-60y - 60z = - 1,650,000 ...... (6)
add equation (5) and (6)
6y + 0 = 88,800
y = 14,800 seats
Input the value of y into equation (4) to find z
2y + 2z = 55,000
2(14,800) + 2z = 55,000
29,600 + 2z = 55,000
2z = 25,400
z = 12,700 seats
To find the number of seats in section A we use equation (2)
x + y + z = 55,000
x +14,800 + 12,700 = 55,000
x + 27,500 = 55,000
x = 27,500 seats
To verify our answer to see if the number of seats in Section A equals the total number of seats in Sections B and C.
total number of seats in Sections B and C = 14,800 + 12,700 = 27,500
so number of seats in section A = B + C
