Test 5 Section 4 Number 23

All we really need to do to nail this question is match a table to a linear function. Unlike some similar questions, the table isn’t labeled with variables and the values aren’t sorted in ascending or descending order, but those are just details! We don’t need to get too creative here; let’s just backsolve through the choices and see which one works best. Remember that r represents the monthly rental price (the rightmost column) and p represents the purchase price in thousands (the middle column).

Let’s drop the first row of values (Clearwater Lane) into choice A:

    \begin{align*}r(p)=2.5p-870\\950=2.5(128)-870\\950=-550\end{align*}

NOPE! That didn’t work. We can eliminate A. Let’s try B:

    \begin{align*}r(p)=5p+165\\950=5(128)+165\\950=805\end{align*}

That’s not quite as ridiculous, but still isn’t close enough. Let’s try C:

    \begin{align*}r(p)=6.5p+440\\950=6.5(128)+440\\950=1275\end{align*}

No way, that’s not even close. Eliminate C. Try D:

    \begin{align*}r(p)=7.5p-10\\950=7.5(128)-10\\950=950\end{align*}

Huh. That’s pretty good! To make sure D is the answer, let’s try a couple other rows of data: Driftwood Drive and Edgemont Street.

    \begin{align*}r(p)=7.5p-10\\1310=7.5(176)-10\\1310=1310\end{align*}

    \begin{align*}r(p)=7.5p-10\\515=7.5(70)-10\\515=515\end{align*}

Both are perfect! That’s enough to satisfy me. D is the answer.

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