Question 149185This question is from textbook
: hi, i need exactly step by step solution, thanks
If the numerator and the denominator of a fraction are increased by 3,the resulting fractions is 3/4.But if the terms of the fractions are decreased by 2,the new fraction is 1/3. Find the original faction?
This question is from textbook
Answer by 24HoursTutor.com(40)   (Show Source):
You can put this solution on YOUR website! Let us assume the numerator to be x and the denominator be y. Let ius write the first situation down in which 3 is added to both. The equation should look like :
(x+3)/(y+3) = 3/4
In the second scenario 2 is subtracted from the same fraction which means our equation should look something like :
(x-2)/(y-2) = 1/3
From our second equation let us find an equation for y in terms of x :
(x-2)/(y-2)=1/3
3(x-2)=1(y-2)We have taken the 3 on the left hand side and the denominator to RHS)
3x-6 = y - 2 {Simply opened the brackets}
3x-6+2 = y { group everything on one side and y on one side}
y = 3x-4
Now we substitute this value of y in our first equation to get a value for x :
(x+3)/(y+3) = 3/4
4(x+3) = 3(y+3) { First, we get both the denominators on the opposite sides to multiply}
4x+12 = 3y + 9 {Simply opened the brackets}
4x+12 = 3(3x-4) + 9 { Substituted the value of y from above }
4x+12 = 9x - 12 + 9 { Opened the brackets }
4x+12 = 9x - 3
4x-9x = -3-12{grouping the x's on one side and the other numbers on one side}
-5x = -15
5x = 15 {removed negative sign from both the sides}
x = 15/5
x = 3
Now substituting the value of x in the equation above to find value of y :
y = 3x-4
y = 3(3) - 4
y = 9-4
y = 5
Therefore, our required fraction is 3/5. Let us check if it holds true for both the situations.
Situation 1 : 3 is added to both numerator and denominator. So. our fraction becomes 6/10 which when reduced would five 3/4. Thus, condition satisfied.
Situation 2 : 2 is subtracted from both the numerator and the denominator. So, our fraction becomes 1/3 which is what we wanted!
Hence, after checking we can confidently say that the required fraction is 3/5
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