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

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) (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.
AND . Those are a system of simultaneous equations. Solve for x and y.

The rational equation can be adjusted,

, which might be more convenient to use. Why?

Because the system is equivalently

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.
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