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# M14-22

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Math Expert
Joined: 02 Sep 2009
Posts: 58340

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16 Sep 2014, 00:53
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Difficulty:

5% (low)

Question Stats:

92% (01:11) correct 8% (01:11) wrong based on 59 sessions

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When two identical liquids are mixed, the temperature of the mix can be found by the formula

$$T = \frac{Q1*T1 + Q2*T2}{Q1 + Q2}$$,

where $$Q1$$ and $$Q2$$ are quantities of liquids being mixed and $$T1$$ and $$T2$$ are temperatures of these liquids.

If the temperature of the mix of $$N$$ liters of 10-degree water with $$2N$$ liters of $$X$$-degree water is 20 degrees, what is $$X$$?

A. 21
B. 23
C. 25
D. 30
E. the data is not sufficient to answer the question

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Math Expert
Joined: 02 Sep 2009
Posts: 58340

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16 Sep 2014, 00:53
1
Official Solution:

When two identical liquids are mixed, the temperature of the mix can be found by the formula

$$T = \frac{Q1*T1 + Q2*T2}{Q1 + Q2}$$,

where $$Q1$$ and $$Q2$$ are quantities of liquids being mixed and $$T1$$ and $$T2$$ are temperatures of these liquids.

If the temperature of the mix of $$N$$ liters of 10-degree water with $$2N$$ liters of $$X$$-degree water is 20 degrees, what is $$X$$?

A. 21
B. 23
C. 25
D. 30
E. the data is not sufficient to answer the question

$$T = \frac{N10 + 2NX}{N + 2N} = \frac{2X + 10}{3} = 20$$. From this equation, $$X = 25$$.

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Joined: 27 Sep 2015
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06 Feb 2016, 11:53
Why is it that you can cancel all the 'N' from the equation T=N10+2NX /N+2N
Math Expert
Joined: 02 Sep 2009
Posts: 58340

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06 Feb 2016, 11:58
mpcroaming wrote:
Why is it that you can cancel all the 'N' from the equation T=N10+2NX /N+2N

T = (N10 + 2NX)/(N+2N) = N(10 + 2X)/(3N) --> reduce by N: (10 + 2X)/3.
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Joined: 26 Mar 2013
Posts: 2345

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06 Feb 2016, 14:06
We can plug-in numbers

Q1=N=1 & Q2=2N=2

20= [(1*10)+ (2*T2)]/3

60= 10 +2T2..........> T2=25

Intern
Joined: 30 Sep 2017
Posts: 15

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17 Dec 2018, 21:12
Where is it mentioned that both liquids are identical?

Bunuel
Re: M14-22   [#permalink] 17 Dec 2018, 21:12
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# M14-22

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