SOLUTION: A 100% concentrate is to be mixed with a mixture having a concentration of 30% to obtain 45 gallons of a mixture with a concentration of 75%. How much of the 100% concentrate will

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Question 714420: A 100% concentrate is to be mixed with a mixture having a concentration of 30% to obtain 45 gallons of a mixture with a concentration of 75%. How much of the 100% concentrate will be needed? (Round your answer to one decimal place.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
"...to obtain 45 gallons of mixture."
Let x and y be the gallons of the 100% concentrate and the 30% strength mixture, respectively, to use.
%281%2Ax%2B0.3y%29%2F45=0.75 AND x%2By=45. Those are a system of simultaneous equations. Solve for x and y.

The rational equation can be adjusted,
x%2B0.3y=45%2A0.75
x%2B0.3y=33.75, which might be more convenient to use. Why?

Because the system is equivalently
x%2B0.3y=33.75
x%2By=45
Subtract the first equation from the second equation and very fast solve for y. Use the value found for y in the second equation to solve for and find the value for x.