Question 473634: Mr. Gebra was 32 when his son Al was born. After 14 years, mr. gebra's age is twice as old as his son Al. What re their present ages?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! For the purpose of writing equations, let's call Mr. Gebra's present age "G" and his son Al's present age "A".
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Since Mr. Gebra was 32 years old when his son Al was born, there is 32 years difference in their present ages. So, if we add 32 years to Al's present age, we get Mr. Gebra's present age. In equation form this can be written as:
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G = A + 32
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and this is our first equation.
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Then we know that 14 years from now Mr. Gebra's age will be twice that of his son Al's age. In 14 years, Mr. Gebra age will be his present age plus 14 years. So Mr. Gebra will be G + 14 years old. And 14 years from now his son will be his present age plus 14 years. So his son will be A + 14. At that time (14 years from now) if you double his son's age it will equal Mr. Gebra's age. So, we can write this in equation form as:
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G + 14 = 2(A + 14)
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This is our second equation.
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By doing the distributed multiplication on the right side this equation becomes:
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G + 14 = 2A + 28
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Get rid of the 14 on the left side by subtracting 14 from both sides of this equation to get:
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G = 2A + 14
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This is the reduced or simplified form of our second equation.
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Now let's return to the first equation where we had G = A + 32. We can substitute this value for G, that is substitute A + 32 in place of G in the reduced form of the second equation. With that substitution the reduced form of the second equation becomes:
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A + 32 = 2A + 14
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We can get rid of the 32 on the left side by subtracting 32 from both sides. When we do that subtraction this equation now becomes:
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A = 2A - 18
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And then we can get rid of the 2A on the left side by subtracting 2A from both sides. That subtraction from both sides results in:
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- A = - 18
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Finally we can change the minus sign on the left side to a positive sign if we multiply both sides of this equation by -1. That multiplication results in the equation becoming:
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+A = +18
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A is Al's present age. And we also know Mr. Gebra's age must be 32 years older than Al. So Mr. Gebra's present age is 18 + 32 or 50 years old.
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As a further check, 14 years from now Al will be 18 + 14 = 32 years old. And 14 years from now Mr. Gebra will be 50 + 14 = 64 years old. Note at that time Mr. Gebra will be twice his son's age ... 64 equals twice 32.
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In summary, Mr. Gebra is presently 50 years old, and his son Al is presently 18 years old.
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Hope this helps you to understand the problem and, more importantly, that you understand the process for analyzing it, writing appropriate equations, and solving them.
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