Question

The sum of the numerator & denominator of a fraction is equal to 7.
4 times the numerator is 8 less than 5 times the denominator.
find the fraction​

Answer 1

Given :

• sum of numerator and denominator = 7
• 4 times the numerator is 8 less than 5 times the denominator

To Find :

• find the fraction ?

Solution :

let the numerator be x and denominator be y then,

$\bold{fraction = \frac{x}{y} }$

now, according to the question

• x + y = 7 .........(i)
• 4x = 5y - 8 .........(ii)

from eq.(i) x + y = 7

➪ x = 7 - y ..........(iii)

now substitute the value of x from (iii) in (ii)

$\bold{: \implies 4(7 - y) = 5y - 8} \\ \\ \bold{: \implies 28 - 4y = 5y - 8 } \: \\ \\ \bold{: \implies 28 + 8 = 5y + 4y} \: \\ \\ \bold{: \implies 36 = 9y} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies y = \cancel\frac{36}{9} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \boxed{ \bold{y = 4}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now, substitute the value of y in (iii)

$\bold{: \implies \: x = 7 - 4 } \\ \\ \bold{: \implies \boxed{ \bold{x = 3}} } \: \: \: \: \:\:$

so, value of x is 3 and value of y is 3

therefore, fraction is $\orange{\bold{\frac{3}{4}}}$