Question

The denominator of a fraction is 1 less than four times the numerator. If 1 is added to both the numerator and the denominator, the fraction becomes 3 by 8

Answer 1

Answer:

The original fraction is 37

Explanation:

Let xy represent the fraction

The problem specifies

(a) Adding 1 to the numerator and denominator makes the fraction equal to 12
(b) Subtracting 1 from the top and bottom makes the fraction equal to 13

(a)  x+1y+1=12

(b)  x−1y−1=13

........................―――――――

Solve for x, already defined as "the numerator of the original equation"

These equations can be solved as Ratio&Proportion problems.

1) Cross multiply both equations
(a)   2(x+1)=1(y+1)
(b)   3(x−1)=1(y−1)

2) Clear the parentheses
(a)   2x+2=y+1
(b)   3x−3=y−1

3) Write the equations with the variables on the left and the numbers on the right
(a)   2x−y= - 1
(b)   3x−y=    2

4) Start with Equation (b) and subtract Equation (a)
(Do it in this order to avoid negative numbers.)
(b)      3x−y=   2 
(a) - (2x−y= - 1)

5) Clear the parentheses and combine to eliminate the y term
(b)     3x−y=2
(a) −2x+y=1
―――――――――
..........x ...m=3 ← already defined as "the numerator of the original fraction"

........................―――――――

Solve for y, already defined as "the denominator of the original fraction"

1) Using one of the original equations, sub in 3 in the place of x 
x−1y−1=13

3−1y−1=13

2) Cross multiply and solve for y, already defined as "the denominator of the original fraction"
3(3−1)=1(y−1)

3) Solve inside the parentheses
3(2)=1(y−1)

4) Clear the parentheses by distributing the 3and the 1
6=y−1

5) Add 1 to both sides to isolate y

6) 7=y ← answer for y, defined as "the denominator of the original fraction"

Answer
The original fraction is 37

Answer 2

You'll find the solution of this question in the attachment above