A publishing company produced a record high of 180 books tod

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A publishing company produced a record high of 180 books today. In the 9 days prior to today, the same publishing company had produced an average (arithmetic mean) of \(x\) books per day. If today's record high increased average daily production to \(y\) books per day, what is \(x\) in terms of \(y\)?


\(A)\quad \dfrac{9y+180}{10}\)

\(B) \quad \dfrac{10y+180}{9}\)

\(C) \quad \dfrac{9y−180}{9}\)

\(D) \quad \dfrac{10y−180}{9}\)

\(E) \quad \dfrac{10y}{9}−10\)

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT
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by GMATGuruNY » Sat Nov 23, 2019 2:56 am
VJesus12 wrote:A publishing company produced a record high of 180 books today. In the 9 days prior to today, the same publishing company had produced an average (arithmetic mean) of \(x\) books per day. If today's record high increased average daily production to \(y\) books per day, what is \(x\) in terms of \(y\)?


\(A)\quad \dfrac{9y+180}{10}\)

\(B) \quad \dfrac{10y+180}{9}\)

\(C) \quad \dfrac{9y−180}{9}\)

\(D) \quad \dfrac{10y−180}{9}\)

\(E) \quad \dfrac{10y}{9}−10\)

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT
Let x = 10 books per day.
Total number of books produced in the 9 days prior = 9*10 = 90.
y = average number of books produced over all 10 days = (180+90)/10 = 27.

The question asks for the value of x=10. This is our target.
Now plug y=27 into the answers to see which yields our target of 10.

Only D works:
(10*27-180)/9 = 90/9 = 10.

The correct answer is D.
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by Scott@TargetTestPrep » Fri Dec 13, 2019 1:08 pm
VJesus12 wrote:A publishing company produced a record high of 180 books today. In the 9 days prior to today, the same publishing company had produced an average (arithmetic mean) of \(x\) books per day. If today's record high increased average daily production to \(y\) books per day, what is \(x\) in terms of \(y\)?


\(A)\quad \dfrac{9y+180}{10}\)

\(B) \quad \dfrac{10y+180}{9}\)

\(C) \quad \dfrac{9y−180}{9}\)

\(D) \quad \dfrac{10y−180}{9}\)

\(E) \quad \dfrac{10y}{9}−10\)

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT
We can create the equation:

(180 + 9x)/10 = y

180 + 9x = 10y

9x = 10y - 180

x = (10y - 180)/9

Answer: D

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