Hi Mick.

Start by assigning variables to the unknowns:

Let B = the number of brown envelopes,
let W = the number of white envelopes,
let w = the cost of one white envelope and
let b = the cost of one brown envelope.

Then translate the question into equation terms:

There were 17 envelopes bought, some were brown, some were white.
   becomes B + W = 17

The brown envelopes cost one cent more per envelope than the white ones.
   becomes b = w + 1

The total cost was 80 cents.
   becomes Bb + Ww = 80

Now we can solve for B using the first equations:

B = 17 - W

And then substitute for b and B in the total cost equation:

(17-W)(w+1) + Ww = 80
which reduces to
W = 17w - 63

which still leaves two variables unresolved. However, we know that W is a whole positive number (we are interpreting the word "some" in the question to mean "at least one") and w is a whole positive number as well.

We also know that W is at most 16 (there must be at least one brown envelope to qualify as "some") and at least 1. So let's write this as an inequality:

1 ≤ W ≤ 16

substituting for W, we have

1 ≤ 17w - 63 ≤ 16
which reduces:
64 ≤ 17w ≤ 79
3.76 ≤ w ≤ 4.64

however, we know w is an integer number of cents, so

w = 4

Finally, we can use this to find W and B:

W = 17w - 63 = 17(4) - 63 = 5
B = 17 - W = 17 - 5 = 12

Always remember to check at the end:

b = w + 1 = 4 + 1 = 5

Bb + Ww = (12)(5) + (5)(4) = 60 + 20 = 80 correct.

Hope this helps,
Stephen La Rocque.