Question

the sum of numerater and denominator of a fraction is 4 more than the twice of numerator if numerator is increased by 3 then the ratio is 2:3 determine the fraction​

Answer 1

Given:

✰ The sum of numerater and denominator of a fraction is 4 more than the twice of numerator.

✰ If numerator and denominator is increased by 3 then the ratio is 2:3.

To determine:

✠ The fraction

Solution:

❖ Let's see the concept first! Here we will assume the numerator of a fraction as x and the denominator of a fraction as y and then we are provided with the conditions and thus we will form linear equations in two variables and after that by using Substitution method we will find out the numerator and denominator of a fraction. We can also solve it by elimination method. Then, we will substitute the value of numerator and denominator in the fraction and can easily determine the required fraction.

Let's determine it...

Let the numerator of a fraction be x,

and the denominator of a fraction be y

Now, the sum of numerater and denominator of a fraction is 4 more than the twice of numerator that means if we add both numerator and denominator of a fraction ( x + y ) their sum will equal to 4 more than that means 4 added to 2 times a numerator.

According to first condition,

➤ x + y = 4 + 2x

➤ y - 4 = 2x - x

➤ y - 4 = x

➤ x - y = - 4

➤ x + 4 = y ...①

If the numerator is increased by 3 that means 3 added to numerater and denominator then the ratio is 2:3.

According to second condition,

➤ x +3/y + 3 = 2/3

➤ 3( x +3 ) = 2( y + 3 )

➤ 3x + 9 = 2y + 6

➤ 3x - 2y = 6 - 9

➤ 3x - 2y = - 3 ...②

Substitute the value of eq① in eq②, we have

➤ 3x - 2 ( x + 4 ) = - 3

➤ 3x - 2x - 8 = - 3

➤ x - 8 = - 3

➤ x = - 3 + 8

➤ x = 5

∴ The numerator of a fraction = 5

Now,

Substituting the value of x in eq①, we have:

➤ x + 4 = y

➤ y = 5 + 4

➤ y = 9

∴ The denominator of a fraction = 9

✵ The Fraction = Numerator/Denominator

✵ The Fraction = 5/9

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