maths

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

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1. 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

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2. How it comes 32

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3. 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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