Question 1129626
1.Half of an integer exceeds one-third of the next integer by unity. Find the integer.
{{{1/2}}}a = {{{1/3}}}(a+1) + 1 
multiply by 6, cancel the denominators
3a = 2(a+1) + 6
3a = 2a + 2 + 6
3a - 2a = 8
a = 8
Check this in the given statement
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2. The denominator of a fraction is 2 more than the numerator
{{{n/((n+2))}}} 
 if 1 is added to both, the fraction is reduced to to 4/5 find the fraction.
{{{(n+1)/((n+2)+1)}}} = {{{4/5}}}
find the fraction.
{{{((n+1))/((n+3))}}} = {{{4/5}}}
cross multiply
5(n+1) = 4(n+3)
5n + 5 = 4n + 12
5n - 4n = 12 - 5
n = 7
{{{7/9}}} is the fraction
Check
Add 1 to both and you get {{{8/10}}} which reduces to {{{4/5}}}
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3.divide 50 into two parts
a + b = 50
 such that if 6 is subtracted from one part and 12 is added to the second part, we get the same number.  
a - 6 = b + 12
a - b = 12 + 6
a - b = 18
Use elimination on these two equations
a + b = 50
a - b = 18
------------addition eliminates b, find a
2a + 0 = 68
a = 68/2
a = 34
then obviously,
b = 16
Check see if this flies in the statement
"if 6 is subtracted from one part and 12 is added to the second part, we get the same number."
34 - 6 = 16 + 12