Wow, this is a toughie!

First, we need to recognize that the purple chips are worth x points, and x must be between 6 and 10 (5<x<11).

Next, you need to prime factorize 88,000 to find how many we have of each chip. As you study more, you'll realize that pretty much any question that says the sum of something = some big number, you need to prime factor.

The prime factors of 88,000 are:

11 (once)
5 (three times)
2 (six times)

Conveniently (and not coincidentally), the values 1, 5, and 11 are represented. So, the purple chips must be worth 2^some power.

Eight is the only number between 6 and 10 that is 2^some power, so, the purple chips must be worth 8 points each.

From our prime factorization, we know that we have six 2's in 88,000. Now, we need to express this in terms of 8s --

2^6 = 8^2

Therefore, there are two purple chips.

Yikes!

good explanation. thanks. now I understand.

ST