SOLUTION: The total mass of a mixture of two liquids is 2.4 kg and the total volume is 1000 cm³ if 1cm³ of one of the liquids weighs 2 grams and 1 cm³ of the other liquid weighs 3 grams w

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Question 1163883: The total mass of a mixture of two liquids is 2.4 kg and the total volume is 1000 cm³ if 1cm³ of one of the liquids weighs 2 grams and 1 cm³ of the other liquid weighs 3 grams what volume of each liquid is present and what mass of each liquid is present.
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343) About Me  (Show Source):
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The total mass is 2400 g, and the density of the mixture is
D = 2400 g/1000 cm^3 = 2.4 g/cc
The mass of liquid 1 is m1 = d1*V1 where d1 and V1 are the density and volume of #1
The mass of liquid 2 is m2 = d2*V2
Given: d1 = 2, d2 = 3
We know that: m1 + m2 = 2400 and V1 + V2 = 1000
Thus m1 = 2V1
2400 - m1 = 3(1000 - V1) -> 2400 - 2V1 = 3000 - 3V1 -> V1 = 600
Hence V2 = 400, m1 = 2*600 = 1200, m2 = 3*400 = 1200
Ans: V1 = 600 cm^3, V2 = 400 cm^3, m1 = m2 = 1200 g



Answer by ikleyn(52775) About Me  (Show Source):
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.

Let x be the volume of the first liquid and y be the volume of the second liquid (in cm^3).



Then the total volume equation is  x +   y = 1000  cm^3,      (1)

while the total mass equation is   2x + 3y = 2400 grams.      (2)



From the first equation  x = 1000 - y.

Substitute it into the second equation.  You will get

    2*(1000-y) + 3y = 2400


Simplify and find y.

    2000 - 2y + 3y = 2400

    y              =  400.


Then from equation (1),  x = 1000-400 = 600.


thus the volumes are  600 cm^3  and  400 cm^3  for the first and the second liquids, respectively.


The masses are  2*600 = 1200 grams  and 3*400 = 1200 grams  (the same masses for both liquids).

Solved, answered and explained.