Question 1178503: The pharmacist needs 70 liters of a 55% saline
solution. The warehouse has barrels of 10% and 80%
saline solutions. How much of each must she mix to
fulfill her request?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source):
Answer by ikleyn(52788)  (Show Source):
You can put this solution on YOUR website! .
Saline solution can not have concentration higher than 27%.
It is well known fact from Science.
See the links
https://en.wikipedia.org/wiki/Saline_(medicine)
https://en.wikipedia.org/wiki/Saline_water
https://en.wikipedia.org/wiki/Brine
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
People who write math problems are not always well versed in science. Ignore the fact that a 55% saline solution is physically impossible; the purpose of the problem is to give the student practice solving "mixture" problems.
If it makes you feel better, change "saline solution" to "antifreeze solution" in the statement of the problem....
(a) Using formal algebra (good practice, if practice with formal algebra is the objective)....
x liters of 10% solution, plus (70-x) liters of 80% solution, yields 70 liters of 55% solution:
Solve using basic algebra; I leave that to you.
(b) Using a method which is much faster and easier than formal algebra (if the speed of getting the answer is important, and formal algebra is not required)....
(1) 55% is 45/70 of the way from 10% to 80%. (picture the three percentages 10, 55, and 80 on a number line, if it helps. From 10 to 55 is 45; from 10 to 80 is 70.)
(2) That means 45/70 of the mixture is the 80% solution.
ANSWER: 45/70 of 70 liters, or 45 liters, of 80%; the other 25 liters of 10%.
CHECK:
.10(25)+.80(45) = 2.5+36 = 38.5
.55(70) = 38.5
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