# SOLUTION: 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 fra

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 fra      Log On

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 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 The above question is solved by one of the experts from 24HoursTutor.com We provide live 1:1 online homework help 1. 24X7 tutors available 2. Certified tutors 3. Only for \$9.99/hr