Missing Number

MISSING NUMBER

Each of the letters in the following expression represents unique numbers. If all the digits 1 through 9 appear exactly once, then find the number represented by each letter:

a / 4 / b
+ / 2 / c / 5
______
d / 1 / e

(Source: Mathematics Teaching in the Middle School, May 1997).

I knew the remaining digits were 3, 6, 7, 8, and 9 because 1, 2, 4, and 5 were already given. Therefore a could only be a 6 or a 7 since 2 + 3 = 5, which is already used; and any number higher than 7 would give you a fourth digit in your answer.

The first time I did this I used 8 = b which made e = 3. This made c = 6 since 4 + 6 + 1 = 11. This made a = 7 and d = 9. Unfortunately I forgot to carry my 1 from the 6 + 4 + 1 = 11.

So I had to go back to the drawing board. I then swap the 3 and the 8 and made c = 7. This made a = 6 and d = 9.

Therefore my problem looked like this:

643

+ 275

918

a = 6

b = 3

c = 7

d = 9

e = 8