A sparkling-water distributor wants to make up 200 gallons of sparkling water to sell for $5.00 per gallon. She wishes to mix th ree grades of water selling for $8.00, $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?
1 answer:
Assuming she make no profit and no loss from the business. Let the number of gallons of the $8 grade water used be x, that of the $3 grade water, y, and that of the $4.50 grade water be z, then: x + y + z = 200 . . . (1) 8x + 3y + 4.5z = 200(5) = 1,000 . . . (2) z = 2y . . . (3) Putting equation (3) into equations (1) and (2), we have: x + y + 2y = 200 or x + 3y = 200 . . . (4) and 8x + 3y + 4.5(2y) = 1000 or 8x + 3y + 9y = 1000 or 8x + 12y = 1000 . . . (5) Multiplying equation (4) by 4, we have: 4x + 12y = 800 . . . (6) Subtracting equation (6) from equation (5), we have: 4x = 200 or x = 200 / 4 = 50 Substituting for x into equation (4), we have: 50 + 3y = 200 or 3y = 200 - 50 = 150 or y = 150 / 3 = 50 Substituting for z into equation (3) gives: z = 2(50) = 100 Therefore, 50 gallons each of the $8 grade water and the $3 grade water should be used and 100 gallons of the $4.50 grade water.
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