Question

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

9

10

11

19

20

Answer 1

(3a+4b)/2<50

Answer 2

All right, so you can assume that \(a = 2b\). Substituting:\[3(2b) + 4b > 50 \]\[6b + 4b >50 \]\[ 10b > 50\]\[ b > 5\]Can you continue it from here?

Answer 3

Also, a=2b
b=a/2

Answer 4

Now, substitute b in (3a+4b)/2<50

Answer 5

Can u?

Answer 6

A little hint:\[b>5\implies 2b>10 \]Remember that we started with \(a = 2b\)?

Answer 7

(3a+4b)/2<50
(3a+4*a/2)/2<50
3a+2a<100
5a<100
a<20

Answer 8

Nope

Answer 9

19

Answer 10

Oops... there was a little mistake in there.

Answer 11

Forgot that we have an arithmetic mean. :)

Answer 12

Yep

Answer 13

its 19