Question

the sum of the numerator and the denominator of a fraction is equal to 7. Four times the numerator is 8less than 5 times the denominator find the fraction

Answer 1

$\textbf{Answer}$

Suppose the denominator of a fraction is x

Since sum of numerator and denominator is 7,

=> Numerator = 7 - x

Four times the numerator = 4(7 - x)
Five times denominator = 5x

$\textbf{According to the question,}$

4(7 - x) = 5x - 8

=> 28 - 4x = 5x - 8

=> 5x + 4x = 28 + 8

=> 9x = 36

=> x = 36/9

=> x = 4

=> 7 - x = 7 - 4 = 3

$\textbf{Numerator of a fraction = 3}$
$\textbf{Denominator of a fraction = 4}$
$\textbf{Fraction = 3/4}$

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Answer 2

Suppose the denominator of a fraction is x

Since sum of numerator and denominator is 7,

=> Numerator = 7 - x

Four times the numerator = 4(7 - x)
Five times denominator = 5x

\textbf{According to the question,}According to the question, 

4(7 - x) = 5x - 8

=> 28 - 4x = 5x - 8

=> 5x + 4x = 28 + 8

=> 9x = 36

=> x = 36/9

=> x = 4

=> 7 - x = 7 - 4 = 3

\textbf{Numerator of a fraction = 3}Numerator of a fraction = 3 
\textbf{Denominator of a fraction = 4}Denominator of a fraction = 4 
\textbf{Fraction = 3/4}Fraction = 3/4