The sum of the numerator and the denominator of a fraction is equal to 7. Four times the numerator is 8 less than 5 times the denominator. Find the fraction.
Linear Equations
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Question

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

KnowledgeBoat · Accepted Answer

Let numerator be x and denominator be y. Given, Sum of the numerator and the denominator of a fraction is equal to 7. ∴ x + y = 7 ⇒ x = 7 - y ..........(1) Given, Four times the numerator is 8 less than 5 times the denominator. ⇒ 5y - 4x = 8 .........(2) Substituting value of x from equation (1) in equation (2), we get : ⇒ 5y - 4(7 - y) = 8 ⇒ 5y - 28 + 4y = 8 ⇒ 9y = 8 + 28 ⇒ 9y = 36 ⇒ y = = 4 Substituting value of y in equation (1), we get : ⇒ x = 7 - 4 = 3. Fraction = . Hence, fraction = .

Mathematics

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

Linear Equations

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