When 10 is added to half the sum of a number and 8, the result is 30. What is the number

2 answers:

5 0

Even though we don't know what the number is, we have to
give it some name, so that we have something to work with.

Now, 16 out of every 19 people will call the number ' X '.
But I like to call it ' M ' instead, for 'Mystery number'.

The mystery number . . . . . M
The sum of the number and 8 . . . M + 8
Half of that sum . . . . . . . . . . . . . . (1/2)(M + 8)
10 added to that sum . . . . . . . . . (1/2)(M + 8) + 10

You said that the result is 30, so I can write:

   (1/2) (M + 8) + 10 = 30

Now, subtract 10
from each side: (1/2) (M + 8) = 20

Multiply each side by 2 :     M + 8 = 40

Subtract 8 from
each side:    M = 32 .

Check to see if that's correct.
Take 32, and do everything to it that the question says:

The number . . . . . . . . . . 32 ?
The sum of the number and 8 . . . 32 + 8 = 40
Half of that sum . . . . . . . . . . . . . . (1/2)(40) = 20
10 added to that sum . . . . . . . . .   20 + 10 = 30

You said that the result is 30, and by golly IT IS !
So the mystery number is really 32.
yay !