SOLUTION: How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 60% antifreeze? Use the six- step method
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Question 1184008: How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 60% antifreeze? Use the six- step method Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52799) (Show Source):
You can put this solution on YOUR website! .
How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 10% antifreeze
to get a mixture that is 60% antifreeze? Use the six- step method
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I don't know what the six-step method is;
therefore, I will solve the problem following to a standard procedure and common sense.
100 gallons of 10% antifreeze contain 0.1*100 = 10 gallons of pure antifreeze.
If we add x gallons of the 70% of the antofreeze solution, the total liquid volume will be 100+x gallons,
and the content of antifreeze in it will be 10+0.7x gallons.
Now, the concentration of the antifreeze in the new mixture is C = gallons of antifreeze
per gallon of the mixture.
It gives an equation to find x
= 0.6.
To solve it, multiply both sides by (100+x) to get
10+0.7x = 0.6*(100+x).
Simplify and find x
10 + 0.7x = 60 + 0.6x
0.7x - 0.6x = 60 - 10
0.1x = 50
x = 50/0.1 = 500.
ANSWER. 500 gallon of the 70% antifreeze solution should be added.
CHECK. = 0.6 = 60%. ! Correct concentration !
Like the other tutor, I have no idea what your "six-step method" is....
For a formal algebraic solution, use what she shows in her response.
Note that, if the numbers are "nice", as they are in this problem, "mixture" problems like this can be solved much faster mentally, like this:
(1) Picture the three percentages 10, 60, and 70 on a number line and observe that 60 is 50/60 = 5/6 of the way from 10 to 70.
(2) That means 5/6 of the mixture is the 70% antifreeze.
(3) So the 100 gallons of 10% antifreeze is 1/6 of the mixture; that means the 5/6 of the mixture that is the 70% antifreeze is 5*100 = 500 gallons.
