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I'm having some trouble with the following task. I've been calculating back and forth on the following equations without getting anywhere.

Sarah is 12 years older than Reed, in 5 years time Sarah is twice the age of Reed 4 years ago, how old are they now?

$Sarah = Reed + 12$
$2(Sarah +5) = Reed -4$

This should be simple enough, still I can't get it. Maybe the calculations I've been doing on these numbers, tried lots of pages, are wrong or the equation is wrong to begin with. Any pointers would be really appreciated.

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I think you mean Sarah + 5 = 2(Reed - 4). :) – Billy Aug 4 '11 at 8:35
Put on dress and $#&! me. Thanks. Put in reply if you want creds. – Algific Aug 4 '11 at 8:35

The First equations is perfect. Coming to the second, the statement says "in 5 years time Sarah is twice the age of Reed 4 years ago", so the equation must be as follows..,


On solving these 2 equations, the age of Sarah is 37 and Reed is 25. Let me know still you dint get!


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The second equation should be (Sarah_Age +5)=2(Reed_Age-4).

There is no difference in the difficulty of solving the original pair of equations or the new pair, if you use algebraic methods (look up "solve system of linear equations"). The result for the original pair has ages that are negative (S = -26, R= -14) so if you were trying to find a solution by guessing particular values for the ages, and using only positive numbers, it would be impossible to find an answer.

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Such questions are easy to work out by making a table like below.

Let $x$ be Reed's current age, then Sarah's age is $x+12$. Filling out values for $+5$ years and $-4$ years in the table gives,

$$ \begin{array}{c c c} & Sarah & Reed \\ \text{4 years ago} & (x+12)-4 & x-4 \\ \text{now} & x+12 & x \\ \text{5 years later} & (x+12)+5 & x+5 \\ \end{array} $$

Now you are given,

in 5 years time Sarah is twice the age of Reed 4 years ago

Using this and values from the table gives,

$$ \begin{align} (x+12) + 5 &= 2(x-4) \\ x + 17 &= 2x - 8 \\ 25 &= x \\ \end{align} $$

Reed's age is, $x = 25$

Sarah's age is, $x + 12 = 25 + 12 = 37$

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