SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50
gallons of a mixture
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-> SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50
gallons of a mixture
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Question 1189846: A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50
gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
First brand ? Gallons
Second brand ? Gallons Found 2 solutions by Theo, greenestamps:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! let x = the amount of solution in the first brand.
let y = the amount of solution in the second brand.
you have two equations that need to be solved simultaneously.
they are:
x + y = 50
.7 * x + .95 * y = .75 * 50
multiply both sides of the first equation by .7 and lease the second equation as is to get:
.7 * x + .7 * y = .7 * 50
.7 * x + .95 * y = .75 * 50
simplify the right side of each equation to get:
.7 * x + .7 * y = 35
.7 * x + .95 * y = 37.5
subtract the first equation from the second to get:
.25 * y = 2.5
solve for y to get:
y = 10
that means x = 40 because 40 + 10 = 50
confirm the solution is correct by replacing x with 40 and y with 10 in both original equations.
x + y = 50 becomes 40 + 10 = 50 which becomes 50 = 50
.7 * x + .95 * y becomes .7 * 40 + .95 * 10 which becomes 28 + 9.5 which becomes 37.5
this confirms the solution is correct.
the solution is 40 gallons of the first brand and 10 gallons of the second brand is required.
The other tutor showed a standard formal algebraic solution; you should understand the method and be able to use it on another similar problem.
That particular tutor usually explains in words everything you need to do to solve the problem, rather than simply showing the calculations. His doing that helps you to see exactly how much work is involved in solving the problem by that method.
Compare that amount of work to the amount of work required with the following solution method, which you can use if formal algebra is not required.
(1) Look at the percentages of the two ingredients and the mixture on a number line -- 70, 75, and 95 -- and observe/calculate that 75 is 5/25 = 1/5 of the way from 70 to 95.
(2) That means 1/5 of the mixture needs to be the 95% antifreeze.
ANSWER: 1/5 of 50 gallons, or 10 gallons, of the 95% antifreeze; the other 40 gallons of the 70% antifreeze.
