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If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p?

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Bunuel
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If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   08 May 2022, 02:41
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If ​\(3p = 4s​, ​\ 5s = \frac{3}{r}​\), and \(r ≠ 0​\), what is r in terms of p?


A. \(\frac{4}{5p​}\)

B.​ \(\frac{4p}{5}​\)

C.​ \(\frac{5p}{4}​\)

D.​ \(\frac{9}{20p}\)​

E.​ \(\frac{45}{4p}\)


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A
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Re: If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   08 May 2022, 15:19
3p = 4s, s= 3p/4.
r = 3/5s, so, r = 4/5p. Option A.
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Re: If 3p = 4s, 5s = 3/r, and r = 0, what is r in terms of p? [#permalink] New post   09 May 2022, 05:57
I was confused as to how r could be zero.
But, if I ignore that, r comes out to be 4p/5 (answer choice B)

Bunuel please advise
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Re: If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   09 May 2022, 10:15
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Bunuel wrote:
If ​\(3p = 4s​, ​\ 5s = \frac{3}{r}​\), and \(r ≠ 0​\), what is r in terms of p?


A. \(\frac{4}{5p​}\)

B.​ \(\frac{4p}{5}​\)

C.​ \(\frac{5p}{4}​\)

D.​ \(\frac{9}{20p}\)​

E.​ \(\frac{45}{4p}\)


Source: Skills Insight

Let , \(5s = \frac{3}{r} = 30\)

So, \(s = 6\) ; \(r = \frac{1}{10}\)

Again, \(3p = 4*6\)

So, \(p = 8\)

Thus, r in terms of p will be

\(\frac{4}{5*8} = \frac{1}{10}\), Hence, Answer must be (A)
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Re: If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   27 Jun 2022, 07:29
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Bunuel wrote:
If ​\(3p = 4s​, ​\ 5s = \frac{3}{r}​\), and \(r ≠ 0​\), what is r in terms of p?


A. \(\frac{4}{5p​}\)

B.​ \(\frac{4p}{5}​\)

C.​ \(\frac{5p}{4}​\)

D.​ \(\frac{9}{20p}\)​

E.​ \(\frac{45}{4p}\)
Source: Skills Insight


Another approach is to rewrite each equation so that they both feature the same multiple of \(s\). Here's what I mean:

Take: \(3p = 4s\)
Create an equivalent equation by multiplying both sides by \(5\) to get: \(15p = 20s\)

Take: \(5s = \frac{3}{r}\)
Create an equivalent equation by multiplying both sides by \(4\) to get: \(20s = \frac{12}{r}\)

Since both equations are set equal to \(20s\), we can create the following equation: \(15p = \frac{12}{r}\)

Multiply both sides of the equation by \(r\) to get: \(15pr = 12\)

Divide both sides of the equation by \(15p\) to get: \(r = \frac{12}{15p}= \frac{4}{5p}\)

Answer: A
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If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   20 Sep 2022, 06:32
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Given that ​3p = 4s​ and 5s = \(\frac{3}{r}​\) and r ≠ 0 and we need to find what is r in terms of p

3p = 4s​

=> 4s = 3p and
5s = \(\frac{3}{r}​\)

Dividing above two equation we get
\(\frac{4s}{5s}\) = 3p / (\(\frac{3}{r}\))
=> \(\frac{4}{5}\) = p*r
=> r = \(\frac{4}{5p}\)

So, Answer will be A
Hope it helps!
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Re: If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink] New post   17 Mar 2024, 21:09
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Re: If 3p = 4s, 5s = 3/r, and r 0, what is r in terms of p? [#permalink]
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