Answer:
The number of empty seats each of these three airlines carried on its flight are as follows:
United Continental = 150 empty seats
American = 50 empty seats
Southwest = 70 empty seats
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.
The explanation of the answers is now provided as follows:
Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:
U + A + W = 270 ………………………. (1)
Since United Continental had three times as many empty seats as American, this implies that:
U = 3A ………………………………… (2)
Substituting U = 3A into equation (1), we have:
3A +A + W = 270
4A + W = 270
W = 270 - 4A ………………………….. (3)
For the cost, we have:
3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990
((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000
((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33
0.447A + 0.146A + 0124W = 38.33
0.593A + 0.124W = 38.33 ………………… (4)
Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:
0.593A + 0.124(270 - 4A) = 38.33
0.593A + 33.48 - 0.496A = 38.33
0.593A - 0.496A = 38.33 - 33.48
0.097A = 4.84
A = 4.84 / 0.097
A = 49.8969072164948
Rounding to a whole number, we have:
A = 50
Substituting A = 50 into each of equations (2) and (3), we have:
U = 3 * 50 = 150
W = 270 - (4 * 50) = 70
Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:
United Continental = 150 empty seats
American = 50 empty seats
Southwest = 70 empty seats
