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?


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+13=2x+10}}}


Subtract 10 from both sides of the equation


{{{x+13-10=2x+cross(10)-cross(10)}}}


{{{x+3=2x}}}


Subtract x from both sides of the equation


{{{cross(x)+3-cross(x)=2x-x}}}


{{{3=x}}} and {{{x+8=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