I am hoping someone can confirm my understanding of the principle behind the answer to this question because I think the explanation in the back of the book is unclear.

Is the average of a and b less than 40?

1. The average of 3a and 3b is 117

3a + 3b/2 = 117

So, I just want to make sure that the principle here is that a+b/2 = 117/3 (or a+b/2 =39) thus less than 40 and it's sufficient?

Thanks

It looks like you have it. I'm going to clarify notation, but I think you're on the right track.

If the average of 3a and 3b is 117, then
(3a+3b)/2 = 117
This means that either
3a + 3b = 234
a+b = 78
OR we might write
(3a+3b)/2 = 117
(a+b)/2 = 117/3
(a+b)/2 = 39
(a+b) = 78

Both, obviously, get us the same place.
And yes, it's sufficient to answer the question.

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