document.write( "Question 149183This question is from textbook
\n" ); document.write( ": Hi i need exactly step by step solution in this word problem,and check it.thanks \r
\n" ); document.write( "\n" ); document.write( "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 fractions is 1/3.Find original fraction. \n" ); document.write( "
Algebra.Com's Answer #109443 by 24HoursTutor.com(40)\"\" \"About 
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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 :\r
\n" ); document.write( "\n" ); document.write( "(x+3)/(y+3) = 3/4\r
\n" ); document.write( "\n" ); document.write( "In the second scenario 2 is subtracted from the same fraction which means our equation should look something like :\r
\n" ); document.write( "\n" ); document.write( "(x-2)/(y-2) = 1/3\r
\n" ); document.write( "\n" ); document.write( "From our second equation let us find an equation for y in terms of x :\r
\n" ); document.write( "\n" ); document.write( "(x-2)/(y-2)=1/3
\n" ); document.write( "3(x-2)=1(y-2)We have taken the 3 on the left hand side and the denominator to RHS)
\n" ); document.write( "3x-6 = y - 2 {Simply opened the brackets}
\n" ); document.write( "3x-6+2 = y { group everything on one side and y on one side}
\n" ); document.write( "y = 3x-4\r
\n" ); document.write( "\n" ); document.write( "Now we substitute this value of y in our first equation to get a value for x :\r
\n" ); document.write( "\n" ); document.write( "(x+3)/(y+3) = 3/4
\n" ); document.write( "4(x+3) = 3(y+3) { First, we get both the denominators on the opposite sides to multiply}
\n" ); document.write( "4x+12 = 3y + 9 {Simply opened the brackets}
\n" ); document.write( "4x+12 = 3(3x-4) + 9 { Substituted the value of y from above }
\n" ); document.write( "4x+12 = 9x - 12 + 9 { Opened the brackets }
\n" ); document.write( "4x+12 = 9x - 3
\n" ); document.write( "4x-9x = -3-12{grouping the x's on one side and the other numbers on one side}
\n" ); document.write( "-5x = -15
\n" ); document.write( "5x = 15 {removed negative sign from both the sides}
\n" ); document.write( "x = 15/5
\n" ); document.write( "x = 3\r
\n" ); document.write( "\n" ); document.write( "Now substituting the value of x in the equation above to find value of y :
\n" ); document.write( "y = 3x-4
\n" ); document.write( "y = 3(3) - 4
\n" ); document.write( "y = 9-4
\n" ); document.write( "y = 5\r
\n" ); document.write( "\n" ); document.write( "Therefore, our required fraction is 3/5. Let us check if it holds true for both the situations.\r
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "Situation 2 : 2 is subtracted from both the numerator and the denominator. So, our fraction becomes 1/3 which is what we wanted!\r
\n" ); document.write( "\n" ); document.write( "Hence, after checking we can confidently say that the required fraction is 3/5\r
\n" ); document.write( "\n" ); document.write( "The above question is solved by one of the experts from 24HoursTutor.com
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