Respuesta :
Answer:
The original fraction is [tex]\dfrac{12}{7}[/tex] .
Step-by-step explanation:
Given as :
Let The original fraction [tex]\dfrac{x}{y}[/tex]
where numerator = x
Denominator = y
Now, The statement are
The numerator exceed the denominator by 5
i.e numerator = 5 + denominator
Or, x = 5 + y ........1
Again
The numerator is decreased by 4 and the denominator is increased by 3, the resulting fraction is equal to 4/5.
So,
[tex]\dfrac{x - 4}{y + 3}[/tex] = [tex]\dfrac{4}{5}[/tex]
Or, 5 × ( x- 4 ) = 4 × ( y + 3 )
Or, 5 x - 20 = 4 y + 12
Or, 5 x = 4 y + 12 + 20
Or, 5 x = 4 y + 32 ........2
Solving equation 1 and 2
Putting the value of x from eq 1 into eq 2
So, 5 × ( 5 + y ) = 4 y + 32
Or, 25 + 5 y = 4 y + 32
Or, 5 y - 4 y = 32 - 25
i.e, y = 7
So, The denominator = y = 7
Now,putting vale of y into eq 2
So, 5 x = 4 × 7 + 32
Or, 5 x = 28 + 32
Or, 5 x = 60
∴ x = [tex]\dfrac{60}{5}[/tex]
i.e x = 12
So, The numerator = x = 12
So fraction [tex]\dfrac{x}{y}[/tex] = [tex]\dfrac{12}{7}[/tex]
Hence, The original fraction is [tex]\dfrac{12}{7}[/tex] . Answer
