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I'd like help with this question:

"Find the error in the statement: The total use of eletricity in a city had declined in one billing period by $5$%,house hold use had declined by $4$% and all other uses increased by $25$%"

thanks.

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Maybe the $4$ needs a % sign? –  night owl Oct 1 '11 at 22:09
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1 Answer 1

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If the total decline was $5$%, and household use declined only $4$%, other use must have declined more than $4$%, but in fact it went up; this is clearly impossible.

If you want to work it out in gory detail, let $h_0$ be the previous household use, $h_1$ the current household use, $x_0$ be the previous other use, and $x_1$ the current other use. The total use has gone from $h_0+x_0$ to $h_1+x_1$. We’re told that $$\begin{align*} h_1 &= 0.96h_0,\tag{1}\\ x_1 &= 1.25x_0,\text{ and}\tag{2}\\ h_1+x_1 &= 0.95(h_0+x_0).\tag{3} \end{align*}$$

Add $(1)$ and $(2)$ and multiply out $(3)$, and compare the results.

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