The positive difference is 3
Let the smaller number be x
Let the larger number be y.
The sum of two numbers is 31. This will be: x + y = 31 ......... equation i
Twice the smaller number is 11 more than the larger number. This will be:
(2 × x) = y + 11
2x = y + 11
2x - y = 11 ....... equation ii
Collect both equations
x + y = 31 ......... equation i
2x - y = 11 ....... equation ii
Add equation i to ii
(x + 2x) + (y - y) = (31 + 11)
3x = 42
Find the value of x
x = 42/3
x = 14
Smallest number is 14
The larger number will be calculated thus:
x + y = 31
14 + y = 31
y = 31 - 14
y = 17
Larger number is 17
The positive difference will be:
= 17 - 14
= 3
In conclusion, the positive difference between the numbers is 3.
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