10's complement of a number statement

问题:

The values of a,x,y if 47x80 is the 10's complement of yaya0 is:

I calculated the 10's complement of yaya0 to be 100,000-yaya0 and then.

   47x80=100,000-yaya0

Now how to find values ?

回答1:

47080 + 100x = 100000 - (10000y + 1000a + 100y + 10a)
52920 = 100x + 10100y + 1010a

==> a = 2 otherwise you won`t get the 2 as tens

50900 = 100x + 10100y

this can be split up in 5 = y and 9 = x + y

so

a = 2
x = 4
y = 5

回答2:

47x80 represents a number where 'x' is the hundreds. So does yaya0 where 'y' represent the 10-thousands and the hundreds and 'a' represents the thousands and the tens.

The rest is obvious.