Question

the sum of the numeratoe and denominator of a fraction os 12.If the denominator is increased by 3 the fraction becomes 1/2.find the fraction​

Answer 1

Step-by-step explanation:

Answer:

I got

5

7

Explanation:

Let call our fraction

x

y

, we know that:

x

+

y

=

12

and

x

y

+

3

=

1

2

from the second:

x

=

1

2

(

y

+

3

)

into the first:

1

2

(

y

+

3

)

+

y

=

12

y

+

3

+

2

y

=

24

3

y

=

21

y

=

21

3

=

7

and so:

x

=

12

−

7

=

5

Answer 2

Answer:

$\large \dfrac{5}{7}$

Step-by-step explanation:

Let the numerator and denominator of a fraction be x and y.

Fraction =  $\large \dfrac{x}{y}$

Given their sum is 12.

x + y = 12

y = 12 - x ....( i )

Now denominator is increased by 3 the fraction becomes 1/2.

$\large \dfrac{x}{y+3} =\dfrac{1}{2}\\\\\\\large 2x=y+3\\\\\\\large y=2x-3 \ ....(ii)$

From equation ( i ) and ( ii ) we get

12 - x = 2 x - 3

12 + 3 = 2 x + x

3 x = 15

x = 5

Now put x = 5 in ( i )

y = 12 - x

y = 12 - 5

y = 7

Thus we get fraction = $\large \dfrac{5}{7}$

Verification:

Sum is 12

So

5 + 7 = 12

Condition satisfied.

When denominator is increased by 3 the fraction becomes 1/2.

5 / 7+3 = 1 / 2

5 / 10 = 1 / 2

1 / 2 = 1 / 2

Hence both condition is satisfied .