# SOLUTION: A sparkling water distributor wants to make up 300 gal of sparkling water to sell for \$6.00 per gallon. She wishes to mix three grades of water selling for \$9.00, \$3.00 and \$4.50 p

Algebra ->  Algebra  -> Inequalities -> SOLUTION: A sparkling water distributor wants to make up 300 gal of sparkling water to sell for \$6.00 per gallon. She wishes to mix three grades of water selling for \$9.00, \$3.00 and \$4.50 p      Log On

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 Click here to see ALL problems on Inequalities Question 54864: A sparkling water distributor wants to make up 300 gal of sparkling water to sell for \$6.00 per gallon. She wishes to mix three grades of water selling for \$9.00, \$3.00 and \$4.50 per gallon, respectively. She must use twice as much of the \$4.50 water as the \$3.00 water. How many gallons of each should she use?Answer by ankor@dixie-net.com(15747)   (Show Source): You can put this solution on YOUR website!A sparkling water distributor wants to make up 300 gal of sparkling water to sell for \$6.00 per gallon. She wishes to mix three grades of water selling for \$9.00, \$3.00 and \$4.50 per gallon, respectively. She must use twice as much of the \$4.50 water as the \$3.00 water. How many gallons of each should she use? : Let x = amt of \$9 water; Let y = amt of \$3 water; Let z = amt of \$4.50 water; : Wants a total of 300 gallons x + y + z = 300 : Write an equation for: "must use twice as much of the \$4.50 water as the \$3.00 water" z = 2y : In the 1st equation substitute 2y for z x + y + 2y = 300 x + 3y = 300 : Write an equation for: "mix three grades of water selling for \$9.00, \$3.00 and \$4.50 per gallon," for a total of 300 gal at \$6 a gallon. 9(x) + 3(y) + 4.5(z) = 6(300) : Substitute 2y for z in the above equation: 9(x) + 3(y) + 4.5(2y) = 6(300) ; Get rid of the brackets and you have: 9x + 3y + 9y = 1800 9x + 12y = 1800 : Use the elimination method, two equations with two unknowns: x + 3y = 300 9x + 12y = 1800 : Mult the 1st equation by 4 and subtract, eliminating y 4x + 12y = 1200 9x + 12y = 1800 ----------------- subtract -5x + 0y = -600 x = -600/-5 x = +120 gal of \$9 water : Use the equation x + 3y = 300 to find y 120 + 3y = 300 3y = 300 -120 y = 180/3 y = 60 gal of \$3 water : Remember "must use twice as much of the \$4.50 water as the \$3.00 water" Therefore we know that here must be 2 * 60 = 120 gal : z = 120 gal of the \$4.50 : Check: 9(120) + 3(60) + 4.5(120) = 6(300) 1080 + 180 + 540 = 1800 + 1800