Question 223970
John is twice as old as his son.  In 42 years, the ratio of their age will be 4:3.  What is the son's current age?



Step 1.  Let x be the age of John's son.


Step 2.  Let 2x be the age of John.


Step 3.  Let x+42 be the age of John's son in 42 years.


Step 4.  Let 2x+42 be the age of John in 42 years.


Step 5.  Then {{{4/3=(2x+42)/(x+42)}}}


Multiply 3(x+42) to both sides of the equation to get rid of denominators


{{{3(x+42)*4/3=3*(x+42)*(2x+42)/(x+42)}}}


{{{(x+42)*4=3*(2x+42)}}}


{{{4x+4*42=6x+3*42}}}


Subtract 4x+3*42 from both sides of the equation


{{{4x+4*42-4x-3*42=6x+3*42-4x-3*42}}}


{{{42=2x}}}  The age of John


Divide by 2 to both sides of the equation


{{{42/2=2x/2}}}


{{{21=x}}}


Step 6.  ANSWER:  The current age of John's son is 21 years old.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J