SOLUTION: Miguel is 8 years older than his brother Juan. Five years from now, he will be twice as old as Juan. How old are the boys now?

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Question 229963: Miguel is 8 years older than his brother Juan. Five years from now, he will be twice as old as Juan. How old are the boys now?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Miguel is 8 years older than his brother Juan. Five years from now, he will be twice as old as Juan. How old are the boys now?

Step 1. Let x be the age of Juan

Step 2. Let x+8 be the age of Miguel since he is 8 years older than Juan.

Step 3. Let x+5 be the age of Juan five years from now.

Step 4. Let x+8+5=x+13 be the age of Miguel five years from now

Step 5. Then x+13=2(x+5) since five years from now Miguel will be twice as old as Juan.

Step 6. Solving x+13=2(x+5) yields the following steps

x%2B13=2x%2B10

Subtract 10 from both sides of the equation

x%2B13-10=2x%2Bcross%2810%29-cross%2810%29

x%2B3=2x

Subtract x from both sides of the equation

cross%28x%29%2B3-cross%28x%29=2x-x

3=x and x%2B8=11.

Now five years from now Miguel will be 16 and Juan will be 8 which is twice as old as Juan and this is a true statement.

Step 7. ANSWER: Juan is 3 years old and Miguel is 11 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