document.write( "Question 1199556: The ratio of sum and the difference of the present age of Vivek and Arvind are 2: 1. Four years ago, this ratio was 3:2. What will be the ratio of their ages after 12 years \n" ); document.write( "

Algebra.Com's Answer #833485 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "let x = Vivek's current age
\n" ); document.write( "let y = Arvind's current age

\n" ); document.write( "The sum of their ages is x+y; the difference of their ages is x-y.

\n" ); document.write( "The ratio of the sum of their ages and the difference of their ages is 2:1

\n" ); document.write( " $\"%28x%2By%29%2F%28x-y%29=2%2F1\"$
\n" ); document.write( " $\"2x-2y=x%2By\"$
\n" ); document.write( " $\"x=3y\"$ [1]

\n" ); document.write( "Vivek's age 4 years ago was x-4; Arvind's age 4 years ago was y-4.
\n" ); document.write( "The sum of their ages 4 years ago was x+y-8; the difference of their ages 4 years ago was (still!) x-y.
\n" ); document.write( "Four years ago, the ratio of the sum of their ages and the difference of their ages was 3:2

\n" ); document.write( " $\"%28x%2By-8%29%2F%28x-y%29=3%2F2\"$
\n" ); document.write( " $\"2x%2B2y-16=3x-3y\"$
\n" ); document.write( " $\"5y-16=x\"$ [2]

\n" ); document.write( "[1] and [2] show two different expressions in terms of y for variable x. Set those two expressions equal to each other and solve for y.

\n" ); document.write( " $\"3y=5y-16\"$
\n" ); document.write( " $\"2y=16\"$
\n" ); document.write( " $\"y=8\"$ [3]

\n" ); document.write( "Use [1] and [3] to find x.
\n" ); document.write( " $\"x=3%288%29=24\"$

\n" ); document.write( "Their current ages are Vivek = x = 24 and Arvind = y = 8.

\n" ); document.write( "Their ages 12 years from now will be Vivek = 24+12 = 36 and Arvind = 8+12 = 20.

\n" ); document.write( "The ratio of their ages 12 years from now will be 36:20 = 9:5

\n" ); document.write( "ANSWER: 9:5

\n" ); document.write( " \n" ); document.write( "

\n" );