the numerator of a fraction is 3 less than its denominator . If 1 is added to the denominator, the fraction is decrease by 1/15 . find the fraction
Answers
Answer:
(2/5),(6/9)
Step-by-step explanation:
Let the denominator be 'x' and denominator be 'y'.
Hence, the fraction is (x/y).
(i)
Given that numerator is 3 less than its denominator.
⇒ x = y - 3
(ii)
Given that if 1 is added to the denominator, the fraction is decrease by 1/15.
⇒ (x/y + 1) = (x/y) - (1/15)
⇒ (y - 3/y + 1) = (y - 3/y) - (1/15)
⇒ 15y(y - 3) =15(y - 3)(y + 1) - y(y + 1)
⇒ 15y²- 45y = 15(y² + y - 3y - 3) - y² - y
⇒ 15y² - 45y = 15y² + 15y - 45y - 45 - y² - y
⇒ 15y² - 45y = 14y² - 31y - 45
⇒ 14y² + 14y - 45 = 15y²
⇒ -y² + 14y - 45 = 0
⇒ y² - 14y + 45 = 0
⇒ y² - 5y - 9y + 45 = 0
⇒ y(y - 5) - 9(y - 5) = 0
⇒ (y - 5)(y - 9) = 0
⇒ y = 5,9.
Substitute y = 5 in (i), we get
⇒ x = 5 - 3
⇒ x = 2
Substitute y = 9 in (i), we get
⇒ x = 9 - 3
⇒ x = 6.
Therefore, the original fraction:
⇒ (2/5), (6/9).
Hope it helps!
Answer:
(2/5),(6/9)
Step-by-step explanation:
Let the denominator be 'x' and denominator be 'y'.
Hence, the fraction is (x/y).
(i)
Given that numerator is 3 less than its denominator.
⇒ x = y - 3
(ii)
Given that if 1 is added to the denominator, the fraction is decrease by 1/15.
⇒ (x/y + 1) = (x/y) - (1/15)
⇒ (y - 3/y + 1) = (y - 3/y) - (1/15)
⇒ 15y(y - 3) =15(y - 3)(y + 1) - y(y + 1)
⇒ 15y²- 45y = 15(y² + y - 3y - 3) - y² - y
⇒ 15y² - 45y = 15y² + 15y - 45y - 45 - y² - y
⇒ 15y² - 45y = 14y² - 31y - 45
⇒ 14y² + 14y - 45 = 15y²
⇒ -y² + 14y - 45 = 0
⇒ y² - 14y + 45 = 0
⇒ y² - 5y - 9y + 45 = 0
⇒ y(y - 5) - 9(y - 5) = 0
⇒ (y - 5)(y - 9) = 0
⇒ y = 5,9.
Substitute y = 5 in (i), we get
⇒ x = 5 - 3
⇒ x = 2
Substitute y = 9 in (i), we get
⇒ x = 9 - 3
⇒ x = 6.
Therefore, the original fraction:
⇒ (2/5), (6/9).