the numerator of a fraction is 8 less than its denominator. if 12 is a

1.	the numerator of a fraction is 8 less than its denominator. if 12 is added to both numerator and denominator, the fraction becomes 11/19.find the fraction
Answer» Given:- ⠀⠀⠀◍ The NUMERATOR of a fraction is 8 ⠀⠀⠀⠀less than its denominator. ⠀⠀⠀◍ If 12 is added to both numerator ⠀⠀⠀⠀and denominator, the fraction ⠀⠀⠀⠀becomes 11/19. ⠀ To FIND:- ⠀⠀⠀◍ The fraction. ⠀ Let:- ⠀⠀⠀◍ Fraction be ⠀⠀⠀◍ $\sf\dfrac{x}{y}$ ⠀ According to the question ⠀⠀⠀✯ x = y - 8⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Eq......... i ⠀⠀⠀✯ $\sf\dfrac{x + 12}{y + 12}$ = $\dfrac{11}{19}$ ⠀ ⠀ Solution:- ⠀⠀⠀✯ 19 (x + 12) = 11 (y + 12) ⠀⠀⠀✯ 19x + 228 = 11 y + 132 ⠀⠀⠀✯ 19x - 11y = 132 - 228 ⠀⠀⠀✯ 19x - 11y = -96 ⠀⠀⠀✯ 19 (y - 8) - 11y = -96 ⠀⠀⠀✯ 19y - 152 - 11y = -96 ⠀⠀⠀✯ 8Y = -96 + 152 ⠀⠀⠀✯ y = $\sf\dfrac{56}{8}$ ⠀⠀⠀✯ y = 7 ⠀ ◍ Putting the value of y in Eq...... i ⠀⠀⠀✯ x = y - 8 ⠀⠀⠀✯ x = 7 - 8 ⠀⠀⠀✯ x = -1 ⠀ ⠀ Answer:- ⠀⠀⠀★ The fraction = $\sf\dfrac{x}{y}$ ⠀⠀⠀★ The fraction = $\sf\dfrac{-1}{7}$

the numerator of a fraction is 8 less than its denominator. if 12 is added to both numerator and denominator, the fraction becomes 11/19.find the fraction

Answer»

Given:-

⠀⠀⠀◍ The NUMERATOR of a fraction is 8 ⠀⠀⠀⠀less than its denominator.

⠀⠀⠀◍ If 12 is added to both numerator ⠀⠀⠀⠀and denominator, the fraction ⠀⠀⠀⠀becomes 11/19.

⠀

To FIND:-

⠀⠀⠀◍ The fraction.

⠀

Let:-

⠀⠀⠀◍ Fraction be

⠀⠀⠀◍ $\sf\dfrac{x}{y}$

⠀

According to the question

⠀⠀⠀✯ x = y - 8⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Eq......... i

⠀⠀⠀✯ $\sf\dfrac{x + 12}{y + 12}$ = $\dfrac{11}{19}$

⠀

Solution:-

⠀⠀⠀✯ 19 (x + 12) = 11 (y + 12)

⠀⠀⠀✯ 19x + 228 = 11 y + 132

⠀⠀⠀✯ 19x - 11y = 132 - 228

⠀⠀⠀✯ 19x - 11y = -96

⠀⠀⠀✯ 19 (y - 8) - 11y = -96

⠀⠀⠀✯ 19y - 152 - 11y = -96

⠀⠀⠀✯ 8Y = -96 + 152

⠀⠀⠀✯ y = $\sf\dfrac{56}{8}$

⠀⠀⠀✯ y = 7

⠀

◍ Putting the value of y in Eq...... i

⠀⠀⠀✯ x = y - 8

⠀⠀⠀✯ x = 7 - 8

⠀⠀⠀✯ x = -1

⠀

Answer:-

⠀⠀⠀★ The fraction = $\sf\dfrac{x}{y}$

⠀⠀⠀★ The fraction = $\sf\dfrac{-1}{7}$