## 4/26/10

### Test 1 Section 7 - #16 (page 418)

This question is a pain. The thing you have to remember to make it easier is that W, X, Y, and Z all have to be integers between 0 and 9 for this to work. Let's look at the rules (and what they tell us):

X = W + Y + Z  -- This tells us X has to be the biggest number.
W = Y + 1 -- This one's obvious: W is bigger than Y, but only by 1.
Z = W - 5 -- This one tells us a LOT, because the lowest Z can be is 0.

Let's start putting things together. Because of the third rule, we know W is either 5, 6, 7, 8, or 9 (otherwise Z would be negative). But it can't be too big, because the second rule says W is only 1 bigger than Y, and the first rule says X equals the sum of all the other letters. Confused yet? If so, do a little guess and check with possibilities for W to see what happens to the other values.

Here's what I'm coming up with:

W = 5. Why?  Because if it was any bigger, like 6, Y would also be bigger, like 5 ( because of the second rule), so X would be bigger than 9 (by the first rule), which can't happen. Once you've got W, the rest sorta fall into place.

Y = 4.  Why?  Because W = 5 and the second rule tells us Y is one less.

Z = 0.  Why?  Because W = 5 and the second rule tells us W - 5 = Z.

X = 9.  Why?  Because the first rule tells us that X is the sum of all the others and 5 + 4 + 0 = 9

Our WXYZ number is 5940.