BTGModeratorVI wrote: ↑Wed Jul 29, 2020 2:53 pm
A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
A. 6
B. 7
C. 8
D. 9
E. 10
Answer:
D
Solution:
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
