If + = and ^
+ ^
= , find the value of ^
+ ^3
Answers
Answer:
Let the fraction be x/y, where x is the numerator and y is the denominator
Fraction becomes 1/3 when 1 is subtracted from the numerator
(x - 1)/y = 1/3
y = 3 (x - 1)
y = 3x - 3 ..Eq..1
It becomes 1/4 when 8 is added to its denominator.
x/(y + 8) = 1/4
Cross multiplication
(y + 8) = 4x
4x = y + 8….Eq 2
Substituting the value of y from Eq. 1 to Eq. 2
4x = y + 8
4x = 3x - 3 + 8
4x - 3x = 5
x = 5
The numerator is 5
Substituting the value of x in Eq. 2 to derive the value of y
4x = y + 8
4 × 5 = y + 8
20 = y + 8
y = 20 - 8
y = 12
The denominator is 12.
The fraction is 5/12
Step-by-step explanation:
Let the fraction be x/y, where x is the numerator and y is the denominator
Fraction becomes 1/3 when 1 is subtracted from the numerator
(x - 1)/y = 1/3
y = 3 (x - 1)
y = 3x - 3 ..Eq..1
It becomes 1/4 when 8 is added to its denominator.
x/(y + 8) = 1/4
Cross multiplication
(y + 8) = 4x
4x = y + 8….Eq 2
Substituting the value of y from Eq. 1 to Eq. 2
4x = y + 8
4x = 3x - 3 + 8
4x - 3x = 5
x = 5
The numerator is 5
Substituting the value of x in Eq. 2 to derive the value of y