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Two solutions of salt water contain 0.08% and 0.23% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.14% salt. How much of each solution should she use?

User Labs
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1 Answer

3 votes

Answer:

0.5 liters of each will make 1 liter of 0.17% salt solution.

Explanation:

Let x = the amount of 0.07% solution

Let y = the amount of 0.27% solution

Both the amounts combined will make one liter.

x + y = 1

0.0007 of the x solution plus 0.0027 of the y solution will make 0.0017 of the 1 liter.

0.0007x + 0.0027y = 1*0.0017

Multiply the whole thing by 10000 to clear that horrid decimal.

7x + 27y = 17

NOW, you have a system of equations.

x + y = 1

7x + 27y = 17

You go about solving it normally. Multiply the first equation by -7, add them together, and solve for y.

-7x - 7y = -7

7x + 27y = 17

-----------------

20y = 10

y = 0.5

Substitute 0.5 for y in the first equation.

x + 0.5 = 1

x = 0.5

Well, if those answers are correct, you can substitute 0.5 for both x and y in the second equation, and it will work.

7(0.5) + 27(0.5) = 17

3.5 + 13.5 = 17

17 = 17

It works.

User Mkeiser
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