Question 1190041
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x = smaller number
x+3 = larger number
This is because of the phrasing 
"The difference between two numbers is three"


In other words, the gap from x to x+3 is exactly 3 units.


Then we turn to the next bit of info your teacher gave you:
"The sum of twice the larger and one-half the smaller is 36"


That translates to this equation:
2*(larger) + 0.5*(smaller) = 36 
2*(x+3) + 0.5*(x) = 36
where I used 0.5 in place of the fraction 1/2 


Let's solve for x
2*(x+3) + 0.5*(x) = 36 
2x+6 + 0.5x = 36 
2.5x+6 = 36 
2.5x = 36-6 
2.5x = 30 
x = 30/2.5 
x = 12 is the smaller value
x+3 = 12+3 = 15 is the larger value


As a check,
2*(larger) + 0.5*(smaller) = 36 
2*(15) + 0.5*(12) = 36 
30 + 6 = 36 
36 = 36
which works out. The answers are confirmed.


Answers: 
Smaller number = <font color=red>12</font>
Larger number = <font color=red>15</font>
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