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
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
3 answers
How it comes 32
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
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
2 answers