Question 261549
Let x = the 10's digit of the numerator
Let y = the units digit 
:
The two digits in the numerator of a fraction are reversed in its denominator. If 1 is subtracted from both the numerator and the denominator, the value of the resulting fraction is 1/2.
{{{(10x+y - 1)/(10y+x - 1)}}} = {{{1/2}}}
Cross multiply
2(10x+y-1) = 10y+x-1)
:
20x + 2y - 2 = 10y + x -1
:
20x - x = 10y - 2y - 1 + 2
:
19x = 8y + 1
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 The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5.
{{{(y-x)/(y+x)}}} = {{{2/5}}}
Cross multiply
5(y - x) = 2(y + x)
:
5y - 5x = 2y + 2x
5y - 2y = 2x + 5x
3y = 7x
y = {{{7/3}}}x 
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Find the original fraction.
Replace y in the 1st equation; 19x = 8y + 1, with {{{7/3}}}x 
19x * 8({{{7/3}}}x) + 1 
:
19x - {{{56/3}}}x + 1
mult by 3
3(19x) = 56x + 3(1)
57x - 56x = 3
x = 3, is the numerator 10's digit
:
Find y:
y = 3({{{7/3}}})
y = 7, is the numerator units digit
:
The original fraction: {{{37/73}}}
:
:
Check by subtracting 1 from the numerator and denominator
{{{36/72}}} = {{{1/2}}}