Question

11. If 1 is subtracted from the numerator and from

the denominator of a fraction, the value obtained
1
is z. If 1 is added to its numerator and to its
denominator, the resulting value is Ž. Find the
fraction.

Answer 1

3/5

Explanation:

Let x be the numerator

Let y be the denominator

1st equation:

(x-1) / (y-1) = 1/2

By simplifying the equation, 2(x-1) = y-1

y = 2(x-1) + 1

2nd equation:

(x+1) / (y+1) = 2/3

By simplifying the equation, 3(x+1) = 2(y+1)

3x + 3 = 2y + 2

2y = 3x + 1

y = (3x + 1) / 2

Substituting the value of y from the 1st equation to the 2nd equation:

1st equation: y = 2(x-1) + 1

2nd equation: y = (3x + 1) / 2

2(x-1) + 1 = (3x+1) / 2

x = 3

After finding the value of x, let's find y using the 2nd equation:

y = (3x + 1) / 2

y = [(3)(3) + 1] / 2

y = 5

Alternatively, we may also find the value of x using the first equation, and the result is still the same:

y = 2(x-1) + 1

y = 2(3-1) + 1

y = 5

CHECKING TIME!!!

Substituting the values of x and y:

Let x be the numerator, x = 3

Let y be the denominator, y = 5

1st equation: (x-1) / (y-1) = 1/2

(3-1) / (5-1) = 1/2

2/4 = 1/2

By simplification, 1/2 = 1/2

2nd equation:

(x+1) / (y+1) = 2/3

(3+1) / (5+1) = 2/3

4/6 = 2/3

By simplification, 2/3 = 2/3