SOLUTION: 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?

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?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
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

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

John's age

Then Tom's age and 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.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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