Math question help me show my work please?

Question

AHBCF+

EBFAF

________

AGGHFE

i know the answer is 100458 but can someone show me the work

Answer 1

if the answer is 100458, then A=1, G=0, H=4, F=5, and E=8. The rest takes to long for me to do.

Answer 2

...AHBCF

+.EBFAF

--------------

AGGHFE

Adding two 5 digit numbers and getting a 6 digit number means that A has to be 1

E has to be either 8 or 9 to add it to 1 and have it be 10

but from the one's column, E is even (2F), so E = 8 and F is either 4 or 9

Since E = 8, that means that A + E = 10 (with a 1 carried from the next column), so G = 0

now we have :

....1HBCF

+..8BF1F

--------------

..100HF8  (where F is either 4 or 9)

try F = 4

....1HBC4

+..8B414

--------------

..100H48  

this means that C = 3  , but there are no combinations of H and B that work with unique digits

therefore, let F = 9

....1HBC9

+..8B919

--------------

..100H98

C = 7, H = 4, and B = 5

you can get C from the 10's column

from the 100s column, you know that H is one less than B (B + 9 = 1H)

from the 1000s column, you know that H + B = 9 (since you're carrying a 1 from the hundredswith a sum of 10, leaving H = 4 and B = 5)

This gives:

....14579

+..85919

--------------

..100498

Answer 3

A=1 because it is the only answer

E have to be even number because F+F=even number, any same number add together is even.

A+E+carry=1+E+carry=1G=AG therefore E=8  because it is only number that is even number, can add to 1 plus 1 carryover result in two number.

F=4 or 9 Since F+F=?8

G=0 because carry+A+E=1+1+8=10=AG

you type the answer wrong F can't not be 5