SOLUTION: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 10 L of a 40% disinfectant solution? 75% solution ?

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Question 519758: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 10 L of a 40% disinfectant solution?
75% solution ? L
25% solution ?
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
When doing mixture or solution problems, focus on how much 'pure' stuff you need.
.
10 liters of 40% disinfectant will have 10*.4 = 4.0 liters of pure disinfectant and 6.0 liters of water (or some other solvent).
.
x = liters of 75% solution to use
y = liters of 25% solution to use
.
however, we know
x + y = 10
so
y = 10-x
.
That approach means we have only one unknown and, therefore, only need one equation to solve it.
.
.75*x + .25(10-x) = .40(10)
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multiply through by 100 to eliminate the decimals
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75x + 25(10-x) = 40(10)
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75x + 250 - 25x = 400
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50x = 150
.
x = 3
.
y = 10-3
y = 7
.
Answer: Mix 3 liters of 75% disinfectant with 7 liters of 25% disinfectant to produce 10 liters of 40% solution.
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Check the answer by checking how much pure stuff you have.
.75*3 = 2.25
.25*7 = 1.75
2.25 + 1.75 = 4.00 liters of pure disinfectant in the 10 liters, which is a 40% solution.
.
Done.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = liters of 75% solution needed
Let = liters of 25% solution needed
given:
= liters of disinfectant in 75% solution
= liters of disinfectant in 25% solution
---------------
(1)
(2)
---------------------------
(2)
(2)
(2)
Subtract (1) from (2)
(2)
(1)

and
(1)
(1)
(1)
3 liters of 75% solution are needed
7 liters of 25% solution are needed
check:
(2)
(2)
(2)
(2)
(2)
OK