Question 16484: The joint ages of A and B is 82 years. In 6 years times A will be twice as old as B was 4 years ago. Determine their ages now ??
please help i'm really confused.... THANKS
Answer by smik(40)   (Show Source):
You can put this solution on YOUR website! Good question. It requires you to change the information into a system of equations. First of all we know that the "joint ages of A and B is 82 years", which gives us: A + B = 82. Secondly we know that "in 6 years time A will be twice as old as B was 4 years ago" giving us: A+6=2(B-4).
Now that we've got the equations, we can manipulate the second one (A+6=2(B-4)) so that it reads: A=2(B-4)-6 (because we want A on its own, so that we can substitute it into the first equation). Simplify the equation and you get: A=2B-14. Now that we've got this, we can substitute it into A+B=82 (for A), so that it reads: (2B-14)+B=82.
Now we simplify this by foiling everything, which gives us: 3B-14=82. Next, we add 14 to both sides to get: 3B=96. Then we divide both sides by 3, to leave us with:
B=32
Now that we know that, we can plug that value of B into the first equation to determine A: A + 32 = 82. And so we add (-32) to both sides, which leaves us with:
A=50
And there it is. Solved.
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