If the average (arithmetic mean) of 3a and 4b is less than 50, and a is twice b, what is the largest integer value of a?

Answer: The largest value of 'a' is less than 20

Step-by-step explanation:

If arithmetic mean of 3a and 4b is less than 50 i. e 3a+4b/2 < 50

3a+4b < 100 ... (1)

If a is twice as b, a = 2b ... (2)

Substituting equation 2 into 1 we have, 3 (2b) + 4b < 100

6b+4b < 100

10b < 100

b < 10

Since a = 2b, a = 2*10 = 20

Therefore the largest value of 'a' is less than 20 which can be 19.9