Question 1178503
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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.<br>
If it makes you feel better, change "saline solution" to "antifreeze solution" in the statement of the problem....<br>
(a) Using formal algebra (good practice, if practice with formal algebra is the objective)....<br>
x liters of 10% solution, plus (70-x) liters of 80% solution, yields 70 liters of 55% solution:<br>
{{{.10(x)+.80(70-x) = .55(70)}}}<br>
Solve using basic algebra; I leave that to you.<br>
(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)....<br>
(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.<br>
ANSWER: 45/70 of 70 liters, or 45 liters, of 80%; the other 25 liters of 10%.<br>
CHECK:
.10(25)+.80(45) = 2.5+36 = 38.5
.55(70) = 38.5<br>