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1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.
2.) Volume of alcohol in the original mixture
quarts
Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
Therefore, 10 quarts of pure alcohol should be added
3.) Original proportion of white paint in the mixture
Let x be the number of gallons of white paint to be added, then
Therefore, 17 gallons of white paint should be added.
4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.
4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.
5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
Therefore, it will take 7.83 hours to get the tank filled up.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.
2.) Volume of alcohol in the original mixture
Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
Therefore, 10 quarts of pure alcohol should be added
3.) Original proportion of white paint in the mixture
Let x be the number of gallons of white paint to be added, then
Therefore, 17 gallons of white paint should be added.
4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.
4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.
5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
Therefore, it will take 7.83 hours to get the tank filled up.