SOLUTION: Paula is 10 years younger than Greg. In 7 years, she will be 10 years more than half as old as Greg. Find their age at present?

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Question 1147435: Paula is 10 years younger than Greg. In 7 years, she will be 10 years more than half as old as Greg. Find their age at present?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

The setup


    


in the post by @josgarithmetic is INCORRECT.


The correct setup is THIS system of two equations


    


To solve the system, substitute my first equation to the second equation to get


    (g-10) + 7 = 10 + .


Next, multiply both sides  by 2 and simplify, step by step


     2*(g-10) + 14 = 20 + (g+7)

     2g - 20 + 14  = 20 + g + 7

     2g - 6        = g + 27

     2g - g        = 27 + 6

      g            = 33.


Thus Greg is 33 years old.              ANSWER


Then Paula is 33-10 = 23 years old.     ANSWER


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