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tiny-mole [99]
3 years ago
15

Container A has 300 grams of salt water with 13% concentration. Container B has 700 grams of salt water with 7% concentration. A

fter we take out a certain amount of solution from Container A and the same amount from container B, we pour what we take out from A into B and vice versa. Now the two containers have the same concentration. How many grams of solution did we take out from each container?
Mathematics
1 answer:
Triss [41]3 years ago
6 0

Answer:

210 grams

Step-by-step explanation:

Simply, the final amount of each container will not be changed because we add and subtract same amount of solution in the end. Therefore final mass of Container A is 300 grams and final mass of Container B is 700 grams.

However if concentration of the both containers is the same, final amont of the salt should have following relation;

\frac{m_{A}}{m_B}=\frac{3}{7}

where m_A is the amount of salt in container A, and m_B is the amount of salt in container B.

Suppose that the x is the amount that we take away from both containers and than pour into other container. For container A, finally we will have (300-x) grams with 13% concentration and x grams with 7% concentration and vice versa. Total amount of salt in container can be written as,

m_A=(300-x)*\frac{13}{100} +x*\frac{7}{100}=\frac{3900-6x}{100}

similarly for container B ,

m_B=(700-x)*\frac{7}{100} +x*\frac{13}{100}=\frac{4900+6x}{100}

if we replace these values in first equation above and solve for the x,

\frac{m_A}{m_B}=\frac{3900-6x}{4900+6x}=\frac{3}{7}

7*3900- 42x=3*4900+18x\\60x=12600\\x=210

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