Question 227094
John's age is 2 years less than three times Paul his son's age. His son Mark is
15 years older than Paul. The sum of their ages is 103. Find the ages of John and his two sons.


Step 1.  Let x be the age of Paul.


Step 2.  Let x+15 be the age of Mark since Mark is 15 years older than Paul.


Step 3.  Let 3x-2 be the age of John since John is 2 years les than 3 times Paul his son's age.


Step 4.  Then, {{{x+x+15+3x-2=103}}} or {{{5x+13=103}}} since the sum of their sages is 103.


Step 5.  Solving yields the following steps for the equation {{{5x+13=103}}}


Subtract 13 from both sides of the equation


{{{5x+13-13=103-13}}}


{{{5x=90}}}


Divide by 5 to both sides of the equation


{{{5x=90}}}


{{{5x/5=90/5}}}


{{{x=18}}}, Then {{{3x-2=52}}} and {{{x+15=33}}}


Check sum of ages:  {{{18+52+33=103}}} which is a true statement.


Step 6.  ANSWER:  John is 52 years old, Mark is 33 years old, and Paul is 18 years old.


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J

http://www.FreedomUniversity.TV