jfdelgado wrote:

A certain logistics company’s fleet consisted of 120 Type A trucks at the beginning of 1970. At the end of each year, starting with 1970, the company retired 3 of the type A trucks and acquired 6 new Type B trucks. How many years did it take before the number of Type A trucks left in the company’s fleet was less than 50 percent of the fleet?

A. 11

B. 12

C. 13

D. 14

E. 15

Since the answer options are between 11 and 15 years, we could do the calculations for 10 years.

Since 3 Type A trucks are retired and 6 Type B trucks are added every year after 1970.

10 years later, we would have 120 - 10(3) = 90 Type A trucks and 10*6 = 60 Type B trucks.

Let the remaining years after 10 years be x.

\(90 - 3x < 60 + 6x\) -> \(-9x < -30\) -> \(x > 10/3\)

The lowest possible integer value for x here is 4.

So when 14 years have passed, there are more type B trucks.

14 years later, there would be 90 - 12 = 78 type A trucks and 60 + 24 = 84 type B trucks.

Therefore, it takes

14 years(Option D) before the number of type A trucks is less than 50% of the trucks

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