Question 68553
How old is frederique and her brother now?
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Given:
Frederique is two years older than her brother.
12 years ago, she was twice as old as he was.
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Representation:
Let F = Frederique's age now
    B = Her brother's age
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Translate the given sentences to mathematical equation
Frederique is two years older than her brother. 
-->F = B + 2  ---> F - B = 2
<br>12 years ago, she was twice as old as he was.  
--> F-12 = 2 (B-12) --> F - 2B =-12
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Solve the systems of equation:

F - B = 2
F - 2B =-12
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Multiply -1 to F - B = 2
-1 (F - B = 2)
    F - 2B = -12
<br>Use Distributive property to simplify
-F + B = -2
F - 2B = -12
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Add the two eqution

-B = -14
{{{highlight (B = 14)}}} --> Her brother's age now
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Substitute 14 for B to F - B = 2
F - 14 = 2
{{{highlight (F = 16)}}} --> Frederique's age now
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You do the checking to check your answer Sustitute F = 16 and B = 14 to both equations.