## A chemist needs to mix up 50 gallons of a 60% acid solution She only has 50% and 75% solutions on hand, How many gallons of each shoul

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## Answers ( )

x= gallons of the 50% solutiony= gallons of the 75% solutionThe total volume of the new mixture is 50 gal, so

x+y= 50Each gal of 50% solution contributes 0.5 gal of acid, and each gal of the 75% solution contributes 0.75 gal of acid. The final mixture needs to have a concentration of 60% acid, which amounts to 0.6*(50 gal) = 30 gal of acid, so

0.5

x+ 0.75y= 30Solve for

xandy:y= 50 –x0.5

x+ 0.75(50 –x) = 300.5

x+ 37.5 – 0.75x= 307.5 = 0.25

xx= 30==>y= 20