SOLUTION: frederique is two years older than her brother. 12 years ago she was twice as old as he was. How old are they now?

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Question 68553This question is from textbook algebra 1
: frederique is two years older than her brother. 12 years ago she was twice as old as he was. How old are they now? This question is from textbook algebra 1

Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!
How old is frederique and her brother now?


Given:
Frederique is two years older than her brother.
12 years ago, she was twice as old as he was.


Representation:
Let F = Frederique's age now
B = Her brother's age


Translate the given sentences to mathematical equation
Frederique is two years older than her brother.
-->F = B + 2 ---> F - B = 2

12 years ago, she was twice as old as he was.
--> F-12 = 2 (B-12) --> F - 2B =-12


Solve the systems of equation:
F - B = 2
F - 2B =-12


Multiply -1 to F - B = 2
-1 (F - B = 2)
F - 2B = -12

Use Distributive property to simplify
-F + B = -2
F - 2B = -12


Add the two eqution
-B = -14
highlight+%28B+=+14%29 --> Her brother's age now


Substitute 14 for B to F - B = 2
F - 14 = 2
highlight+%28F+=+16%29 --> Frederique's age now


You do the checking to check your answer Sustitute F = 16 and B = 14 to both equations.