Question 1154011
Let the smallest number be x and largest be y

Given that 
Two times the smallest is 4 less than the largest,
{{{2x = y - 4}}} --- (1)
sum of the largest and smallest is 10
{{{x + y = 10}}} ---- (2)

Let us solve the 2 simultaneous equations above.

(1) can be rewritten as
{{{2x - y = -4}}} --- (3)

We have a +y in (2) and a (-y) in (3) so we can eliminate y by adding the 2 equations.

Adding (2) and (3) gives
{{{x + y + 2x - y = 10 - 4}}}
{{{3x = 6}}} or {{{x = 2}}}

Since {{{x + y = 10}}}, {{{y = 8}}}
So the smallest number is 2, largest is 8

Also given that sum of 3 numbers is 17. Let the middle number be m.
{{{2 + m + 8 = 17}}} gives {{{m = 7}}}

So the 3 numbers are {{{2}}} {{{7}}} and {{{8}}}