Question

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

Answer 1

Too long didn't read: answer is 15/33

x/(2x+3)
(X-1)/(2x+3-1)-->(2x+2)
(X-1)/(2x+2)=7/16
It says "simplified result is 7/16"
So what is equal to 7/16 not simplified?

You can try multiplying it by 2 (just an unsimplified version of 7/16)
14/32

So (x-1)/(2x+2)=14/32

Now test it.
X-1 corresponds with 14, so:
X-1=14
X=14+1
X=15

2x+2 corresponds with 32, so :
2*15=30
30+2=32

This proves that they're equal, so x=15. However, you don't want what x is equal to, don't get mixed up. You want the original fraction.

Now simply use the original equation and plug in 15's

X/(2x+3)

X=15, therefore

X/(2x+3)=15/33

Too long didn't read: answer is 15/33

Answer 2

15/33

Explanation:

Let x represent the numerator of the original fraction. Then that fraction is ...

... x/(2x+3)

Decreasing numerator and denominator by 1 gives ...

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

Multiplying by the product of the denominators, we get ...

... 16(x -1) = 7(2x +2)

... 16x -16 = 14x +14 . . . . eliminate parentheses

... 2x = 30 . . . . . . . . . . . add 16-14x

... x = 15 . . . . . . . . . . . . divide by 2

And the original fraction is

... 15/(2·15+3) = 15/33