SOLUTION: 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

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Question 261549: 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. The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5. Find the original fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
%2810x%2By+-+1%29%2F%2810y%2Bx+-+1%29 = 1%2F2
Cross multiply
2(10x+y-1) = 10y+x-1)
:
20x + 2y - 2 = 10y + x -1
:
20x - x = 10y - 2y - 1 + 2
:
19x = 8y + 1
:
The fraction whose numerator is the difference and whose denominator is the sum of the units and tens digits equals 2/5.
%28y-x%29%2F%28y%2Bx%29 = 2%2F5
Cross multiply
5(y - x) = 2(y + x)
:
5y - 5x = 2y + 2x
5y - 2y = 2x + 5x
3y = 7x
y = 7%2F3x
:
Find the original fraction.
Replace y in the 1st equation; 19x = 8y + 1, with 7%2F3x
19x * 8(7%2F3x) + 1
:
19x - 56%2F3x + 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%2F3)
y = 7, is the numerator units digit
:
The original fraction: 37%2F73
:
:
Check by subtracting 1 from the numerator and denominator
36%2F72 = 1%2F2