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we have the given equtaion:

$6000 = bu + 4000$

We are trying to find the value of $600,000 + 100bu +400,000$ given the equation above, there fore i manipulated it by adding $99bu + 396000 + 600000$ to both sides of the eqation giving me:

$600000 + 100bu + 400000 = 606000 + 99bu +396000$

After simplifying the right side i got my answer:

$600000 + 100bu + 400000 = 1002000 + 99bu$

However this was wrong and the value to $600000 + 100bu + 400000$ is equal to $1.2$ million.

Where was my reasoning flawed?

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  • $\begingroup$ Wouldn't combining "like terms" 600,000 and 400,000 be the very first step? It seems strange that these would not be added. But how did you get to that expression from the "given equation" $6000 = (b)(u) + 4000$? I don't get the relationship. $\endgroup$ – hardmath Aug 11 '18 at 1:42
  • $\begingroup$ i added 99bu + 396000 + 600000 to the right side of the original equation to get it in terms of (600,000 + 100bu +400,000). But I added the same quantity to the other side so the equality would hold. $\endgroup$ – Not Friedrich gauss Aug 11 '18 at 1:44
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Note that $bu=2000$, hence $1002000+99(2000)=1.2$ million. So nothing is wrong, just that you are not representing it explicitly.

Alternative computation: $$600,000 + 100bu +400,000=100(6000+bu+4000)=100(6000+6000)$$

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$6000 = bu + 4000$

$bu+4000-4000=6000 - 4000$

$bu=6000-4000=2000$

$600000 + 100bu + 400000 = 1002000 + 99bu=1002000 + 99\times2000=1200000$

So you did nothing wrong. You just need to add the extra steps described above.

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