Question

A company with offices in Anchorage, Alaska wants to lease 10 small planes to fly a group of clients to Nome for a summer fishing trip. They can choose from 6, 8 and 10-passenger planes. The trip will include 84 passengers, total. Find the 5 solutions for how many of each type of plane could be leased? (please show your work)

Answer 1

The solutions of the equations of the situation can be:

z = 1 , y = 5, x = 4

z= 2 , y = 3, x = 5

z=3 , y = 1, x = 6

z = 0 , y = 7, x =3

The question can be expressed as a equation

6 x + 8 y + 10 z = 84

also, x + y + z = 10

⇒ x = 10- y - z

Putting it in first equation,

6(10 - y - z ) +8y + 10z = 84

⇒ 60 +2y + 4z = 84

⇒2(y + 2z ) = 14

⇒ y + 2z = 7

Now putting

z = 1 , we get y = 5,

z= 2 , y = 3

z=3 , y = 1

z = 0 , y = 7

So, only 4 possible solutions.

Therefore, there can only be 4 possible solutions for the equations.

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