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The equation (M + 6)/36 = (p – 7)/21 relates two temperature

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SimaQ
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The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   Updated on: 10 Oct 2013, 02:09
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The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18
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E

Originally posted by SimaQ on 19 Oct 2006, 10:32.
Last edited by Bunuel on 10 Oct 2013, 02:09, edited 1 time in total.
Edited the question and added the OA.
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[#permalink] New post   19 Oct 2006, 13:40
(E) if the typo 7/12 is adapted to 12/7. :)

(M+6)/36=(p-7)/21
<=> M+6 = 36*(p-7)/21
<=> M = 12/7*p - 18
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[#permalink] New post   19 Oct 2006, 14:48
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21(M+6)=36(p-7)
21M+21(6)=36p-36(7)
3M+3(6)=36p/7 - 36
3M=36p/7 - 54
M=12p/7 - 18
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Re: The equation (M+6)/36=(p-7)/21 relates two temperature [#permalink] New post   09 Oct 2013, 19:19
I am not an expert. But this is what I get

m+6/36 =p-7/21 ----> Do cross multiply

21(m+6) = 36(p-7)
21m +126 = 36p - 252
21m = 36p - 252- 126
21m = 36p - 378
m = 36p - 378/21
m = 36p/21 - 378/21
m = 12p/7 - 18

I don't know if I did the process correctly but I got the right answer anyway.
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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   10 Oct 2013, 02:15
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SimaQ wrote:
The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18


NOTE: EDITED THE OPTIONS.

\(\frac{M + 6}{36} = \frac{p - 7}{21}\);

\(M+6=\frac{12}{7}(P-7)\);

\(M+6=\frac{12}{7}P-12\);

\(M=\frac{12}{7}P-18\).

Answer: E.
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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   26 Nov 2015, 16:58
Expert Reply
HI All,

This question can be solved by TESTing VALUES. With the equation (M + 6)/36 = (p – 7)/21, we should look to make the fractions as 'simple' as possible.

When M = 30, we have...

(36)/36 = (P-7)/21

...so P = 28

Among the 5 answer choices, we're looking for one that gives us an M=30 when we plug in P=28. There's only one answer that matches...

Final Answer:
Show Spoiler
E


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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   09 May 2019, 18:15
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SimaQ wrote:
The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18


We need to isolate M:

(M + 6)/36 = (P - 7)/21

21(M + 6) = 36(P - 7)

7(M + 6) = 12(P - 7)

7M + 42 = 12P - 84

7M = 12P - 126

M = (12/7)P - 18

Answer: E
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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   09 May 2019, 18:38
SimaQ wrote:
The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18


Another way:

(M + 6)/36 = (p – 7)/21

(M + 6)/12 = (p – 7)/7

(M + 6)/36 = (p – 7)/21

When P= 7 then M=-6

Apply in each option, only one fits

Answer: E
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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   10 May 2020, 01:43
SimaQ wrote:
The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18


Given: The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale.

Asked: Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(M + 6)/36 = (p – 7)/21
M + 6 = 36(p-7)/21 = (12/7)(p-7) = (12/7)p - 12
M = (12/7)p - 18

IMO E
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Re: The equation (M + 6)/36 = (p – 7)/21 relates two temperature [#permalink] New post   10 May 2020, 01:48
SimaQ wrote:
The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18


Given: The equation (M + 6)/36 = (P – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale.

Asked: Which of the following equations can be used to convert temperatures from the P scale to the M scale?

\(\frac{(M + 6)}{36} = \frac{(P – 7)}{21}; M + 6 = (\frac{36}{21})(P-7) = (\frac{12}{7})P - 12; M = (\frac{12}{7})P -18\)

IMO E
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Re: The equation (M + 6)/36 = (p 7)/21 relates two temperature [#permalink] New post   04 Jul 2023, 04:29
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Re: The equation (M + 6)/36 = (p 7)/21 relates two temperature [#permalink]
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