A certain airline's fleet consisted of 60 Type A planes at the

We are given that the fleet started with 60 type A planes. We are also given that the airline retired 3 of the type A planes and acquired 4 new type B planes each year. We need to determine how many years it took for the number of type A planes left in the airline's fleet to be less than 50 percent of the fleet. We can let n = the number of years it will take for this to occur.

The number of type A planes in the fleet can be expressed as 60 - 3n (because the fleet loses 3 type A planes each year). The total number of planes in the fleet is 60 - 3n + 4n, which takes into account the loss of 3 type A planes and addition of 4 type B planes each year.

We are interested in the number of years it will take until the number of type A planes is less than ½ the total planes in the fleet, as illustrated in the following equation:

60 - 3n < (60 - 3n + 4n) x ½

Multiplying the entire equation by 2, we have:

120 - 6n < 60 + n

-7n < -60

n > -60/-7

n > 8 4/7

Since n > 8 4/7, the smallest integer value n can be is 9.

Answer: D