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A certain airline's fleet consisted of 60 type A planes at the beginni
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10 Apr 2022, 04:13
10 Apr 2022, 04:13
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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
A. 6
B. 7
C. 8
D. 9
E. 10
Re: A certain airline's fleet consisted of 60 type A planes at the beginni
[#permalink]
10 Apr 2022, 19:38
10 Apr 2022, 19:38
1
Quote:
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?
For Type A:
at the end of the 1st year, number of planes are 60
at the end of the 2nd year, number of planes are 60 - 3
at the end of the 3rd year, number of planes are 60 - 3(2)
at the end of the nth year, number of planes are 60 - 3(n-1)
For Type B:
at the end of the 1st year, number of planes are 4
at the end of the 2nd year, number of planes are 4*2
at the end of the 3rd year, number of planes are 4*3
at the end of the nth year, number of planes are 4*n
Total planes at the end of the nth year = 60 - 3(n-1) + 4*n
As per the condition:
60 - 3(n-1) < 1/2 [60 - 3(n-1) + 4*n]
Solving the inequality
n > 8.5
Hence, n = 9
IMO D
Re: A certain airline's fleet consisted of 60 type A planes at the beginni
[#permalink]
02 May 2022, 00:26
02 May 2022, 00:26
kapil1 wrote:
Quote:
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?
For Type A:
at the end of the 1st year, number of planes are 60
at the end of the 2nd year, number of planes are 60 - 3
at the end of the 3rd year, number of planes are 60 - 3(2)
at the end of the nth year, number of planes are 60 - 3(n-1)
For Type B:
at the end of the 1st year, number of planes are 4
at the end of the 2nd year, number of planes are 4*2
at the end of the 3rd year, number of planes are 4*3
at the end of the nth year, number of planes are 4*n
Total planes at the end of the nth year = 60 - 3(n-1) + 4*n
As per the condition:
60 - 3(n-1) < 1/2 [60 - 3(n-1) + 4*n]
Solving the inequality
n > 8.5
Hence, n = 9
IMO D
Could you please elaborate on solving the inequality?
