Respuesta :
Answer:
9 Airbus planes, 1 Boeing plane & 4 Lockheed airplanes
Explanation:
We will develop equations from the information provided
Let the planes be tagged as seen below:
Airbus = x, Boeing = y, Lockheed = z
From the cost of the planes, we have:
200 x + 125 y + 200 z = 2900 ---Eqn 1
From the number of passenger seats, we have:
320 x + 250 y + 275 z = 4480 ---Eqn 2
Twice as many Lockheed airplanes as Airbus planes
⇒ 2z = x ---Eqn 3
Substitute x = 2z into Eqn 1, we have:
200 (2z) + 125 y + 200 z = 2900
125 y + 400 z + 200 z = 2900
125 y + 600 z = 2900 ---Eqn 4
Substitute x = 2z into Eqn 2, we have:
320 (2z) + 250 y + 275 z = 4480
250 y + 640 z + 275 z = 4480
250 y + 915 z = 4480 ---Eqn 5
Multiply Eqn 4 by 2
125 y * 2 + 600 z * 2 = 2900 * 2
⇒ 250 y + 1200 z = 5800 ---Eqn 6
(250 y + 915 z = 4480) ---Eqn 5
Subtracting Eqn 5 from Eqn 6, we have:
250 y - 250 y + 1200 z - 915 z = 5800 - 4480
285 z = 1320
z = 4.6
Substitute z to Eqn 3, x = 2z
⇒ x = 2 * 4.6 = 9.2
x = 9.2
Substitute x & z into Eqn 1
200 x + 125 y + 200 z = 2900
200 * 9.2 + 125 y + 200 * 4.6 = 2900
125 y = 2900 - (1840 + 920)
125 y = 140
y = 1.1
Since it is airplanes that are to be bought, the value of x, y & z must be integers (you cannot buy 4.6 airplanes). As such, we will round down values of airplanes to be bought sodo that we will not exceed the budget.
x = 9, y = 1, z = 4
∴That implies that I will buy 9 Airbus planes, 1 Boeing plane & 4 Lockheed airplanes
