SOLUTION: If 100 gallons of a 75% glycerin solution is made up by conbinding a 30% glycerin soulition with a 90% glycerin solution, how many gallons of each a solution must be used??

Question 801838: If 100 gallons of a 75% glycerin solution is made up by conbinding a 30% glycerin soulition with a 90% glycerin solution, how many gallons of each a solution must be used??
Answer by wilft1(217) (Show Source): You can put this solution on YOUR website!
this will use 2 equations, solved using the addition method
x + y = 100
30x + 90y = 75
start by multiplying 100 x 75 and putting the answer in the bottom equation...
x + y = 100
30x + 90y = 7500
now, time to get rid of one of the variables, lets get rid of x by multiplying the top line by -30 and adding the two lines together...
-30x - 30y = -3000
30x + 90y = 7500
...................
60y = 4500
divide both sides by 60
y = 75
now we know the value for y, lets plug that number into the original equation to find the value of x
30x + 90(75) = 7500
30x + 6750 = 7500
subtract 6750 from both sides
30x = 750
divide both sides by 30
x = 25
so now we know, 25 gallons of 30% solution and 75 gallons of 90% solution.
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