If 5 is added to both the numerator and the denominator of a fraction, the result is equivalent to 3/4. If 3 is subtracted from both the numerator and the denominator of the original fraction, the new result is equivalent to 1/4. Find the original fraction -Using Simultaneous Equations (Can either be the elimination/substitution method)
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Ori fraction x/y
x+5 / y+5 = 3/4, x-3 / y-3 = 1/4
4x-3y=-5
4x-y=9 gives 4x=y+9, replace in above
y+9--3y=-5, y=7; then 4x=16, x=4
Check: 4+5 / 7+5 = 9/12 = 3/4; 4-3 / 7-3 = 1/4.
Ori fraction: 4/7.
x+5 / y+5 = 3/4, x-3 / y-3 = 1/4
4x-3y=-5
4x-y=9 gives 4x=y+9, replace in above
y+9--3y=-5, y=7; then 4x=16, x=4
Check: 4+5 / 7+5 = 9/12 = 3/4; 4-3 / 7-3 = 1/4.
Ori fraction: 4/7.