Each letter in the subtraction problem below represents a different digit from 0 through 9. The digits 3 and 5 do not appear in the problem. Replace each letter so that the answer to the subtraction problem is correct.

GRAPE
- PLUM
________
APPLE

Why would you want someone to work this for you? Hint: A is one less than G. Then look at R-P? what is their relationship?

G=9 R=4 A=8 P=7 E=2 L=1 U=6 M=0

To solve this subtraction problem, we need to find the values of each letter that make the equation valid. Let's break it down step by step:

1. From the hint, we know that A is one less than G. So, let's assign a value for G. Since G cannot be 0, it can be either 6 or 7. For simplicity, let's choose 7.

2. Now, we can determine the value of A. Since A is one less than G, A must be 6.

3. Next, let's examine the relationship between R and P. Since R-P equals a positive value (the difference between two numbers), we know that R must be greater than P. Additionally, since the value of G is 7, the largest possible digit for R is 9 (since we've excluded 3 and 5). Therefore, P must be either 0, 1, or 2.

4. Now let's try to determine the value of E. The result of the subtraction problem is "APPLE," which implies that L - E should be equal to L. Since L cannot be 0 and L - E cannot be equal to 0, E must be 0.

5. Now, we have P = 0. To find the remaining values, we can substitute them into the subtraction problem:

GRAPE
- PLUM
________
A 0 0 6

With E = 0, the equation becomes:

GRA7P
- PLUM
________
A 0 0 6

Rearranging, we now have:

7A7P
- P0UM
________
A 0 0 6

Since P is 0, we have:

7A70
- 0UM
________
A 0 0 6

6. From the right column, we can determine that M must be 4. This is because 0 - 4 = -4, which will result in 6 in the ones place.

7. Now, we can rearrange the equation again:

7A70
- 04U4
________
A 0 0 6

8. Looking at the second column from the right, we can determine that U must be 8. This is because after subtracting 4 from 7, the result will be 3, which will carry to the leftmost column.

9. Rearranging the equation one final time:

7A70
- 0484
________
A 0 0 6

10. Finally, looking at the third column from the right, we can determine that R must be 9. This is because 7 - 4 = 3, which will carry to the leftmost column.

11. Therefore, the values for each letter are:

G = 7
R = 9
A = 6
P = 0
E = 0
L = 1
U = 8
M = 4

When these values are substituted into the subtraction problem, the equation will be correct:

7 6 7 0
- 1 8 4
________
6 0 0 6