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A typical monthly water bill in Bellingham consists of a fixed fee, plus a charge for each $100$ cubic foot (ccf) of water used. $1$ ccf ($100$ cubic foot) = $748$ gallons. A household using $10$ ccf is billed $\$54.92$ whereas a household using $15$ ccf is billed $\$65.77$.

How much water is used by a household that incurs a bill of $\$100$? Round to $2$ decimal figures and use ccf units.

I am confused since $54.92/10$ and $65.77/15$ are different amounts, so the cost per $1$ ccf is different for each. help??

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up vote 1 down vote accepted

HINT: You’re forgetting the fixed fee. Let it be $x$ dollars, and let $y$ be the cost in dollars per ccf. Then $x+10y=54.92$ and $x+15y=65.77$. Subtracting the first equation from the second yields the equation $5y=10.85$, or $y=2.17$. To finish the job, just solve for $x$, and then solve $x+yz=100$ for $z$, using the known values of $x$ and $y$.

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