Posted by **Anonymous** on Friday, February 1, 2013 at 1:52am.

The sum of the digits of a two digit number is multiplied by 8. The result is 8 more than the 2-digit number. Find the

number

- maths -
**Anonymous**, Friday, February 1, 2013 at 3:43am
If the digits are a and b,

8(a+b) = 8+10a+b

8a+8b = 8+10a+b

7b - 2a = 8

The number is 32

- maths -
**Anonymous**, Friday, February 1, 2013 at 5:00am
How it comes 32

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**Reiny**, Friday, February 1, 2013 at 8:44am
from the above

7b - 2a = 8

2a = 7b-8

a = (7b-8)/2

but a and b can only be a numbers between 0 and 9

and since 7b-8 is divided by 2, the expression

7b-8 must be even.

This means that b must be an even number

let's try values of b

let b=2

a = (14-8)/2 = 3

giving us 32

let b=4

a = (28-8)/2 = 10 , but that is too large, and will only get larger if we pick higher values of b

so all done, the number is 32

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