The denominator of a fraction is three more than twice the numerator. if both numerator and denominator are decreased by one, the simplified result is 7/16. find the original fraction.

Old Condition
Numerator = n = x
denominator = d = 2n + 3

New Condition
(x - 1) /(2x + 3 - 1) = 7 / 16
(x - 1) / (2x + 2) = 7 / 16 

Cross multiply and solve
16*(x - 1)  = 7 * (2x + 2) Remove the brackets.
16x - 16 = 14x  + 14 Add 16 to both sides.
16x = 14x + 30 Subtract 14x from both sides.
2x = 30 Divide by 2
x = 15

You really should check this.
Original fraction
15/33
Now subtract 1 from the top and bottom.
14/32 Divide both by 2
7 / 16 which checks out perfectly