SOLUTION: A pharmacist is mixing an 4.7% saline solution and an 19% saline solution to get 3.2 litres of a 8.6% solution. How much of the 19% solution is needed?
Express your answer correct
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Express your answer correct
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Question 1135490: A pharmacist is mixing an 4.7% saline solution and an 19% saline solution to get 3.2 litres of a 8.6% solution. How much of the 19% solution is needed?
Express your answer correct to three significant digits. Answer by ikleyn(52787) (Show Source):
There are several ways to solve it.
One way is to solve the system of 2 equations
x + y = 3.2 for the total volume of two solutions (in liters) (1)
0.047x + 0.19y = 0.086*3.2 for the mass of salt (in kilograms) (2)
You may use the Elimination method. For it, multiply eq(1) by 0.047 (both sides). Keep eq(2) as is. You will get
0.047x + 0.047y = 0.047*3.2 (3)
0.047x + 0.19y = 0.086*3.2 (4) ( same as (2) )
Now subtract eq(3) from eq(4). You will get
(0.19y - 0.047y) = 0.086*3.2 - 0.047*3.2
which gives you y = .
Now I copy this formula in MS Excel in my computer and get the answer in one click: y = 0.873.
Then from eq(1), x = 3.2 - 0.873 = 2.327.
Answer. 2.327 liters of the 4.7% solution and 0.873 liters of the 19% solution.
Solved.
Notice that in the course of my solution I didn't make intermediate calculations.
It is simply in order for do not spend my efforts for nothing.
Instead, I collected everything into the final formula.
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explained at different levels of detalization, from very detailed to very short.
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