Question 226119
Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three years ago Mary was twice as old as John. How old is each now?


Step 1.  Let x be the age of John.


Step 2.  Let x+4 be the age of Tom since Tom is 4 years older than John


Step 3.  Let x+4+3=x+7 be the age of Mary since she is 3 years old than Tom


Step 4.  Let x+4+3-3=x+4 be the age of Mary three years ago


Step 5.  Let x-3 be the age of John three years ago.


Step 6.  Then, x+4=2(x-3) since three years ago Mary was twice as old as John


Step 7.  Solving equation in Step 6 yields the following steps


{{{x+4=2x-6}}}


Add 6-x to both sides to get numbers only on one side and the variable x on the other side.


{{{x+4+6-x=2x-6+6-x}}}


{{{10=x}}}  John's age


Then {{{x+4=14}}} Tom's age and {{{x+4+3=17}}} Mary's age.


Check...if equation in Step 6 is true.  Three years ago Mary was 14 years old which is twice the age of John who was 7 years old which satisfies Step 6.


Step 8.  ANSWER:  John is 10 years old, Tom is 14 years old and Mary is 17 years old.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J