Me on these problems, its urgent! ( for any of these would be greatly appreciated! )
1. a grocer mixes two grades of coffee which sell for 70 cents and 80 cents per pound, respectively. how much of each must he take to make a mixture of 80 pounds which he can sell for 76 cents per pound?
2. how many quarts of pure alcohol must be added to 40 quarts of a mixture that is 35% alcohol to make a mixture that will be 48% alcohol?
3. if a container contains a mixture of 5 gallons of white paint and 11 gallons of brown paint, how much white paint must be added to the container so that the new mixture will be two-thirds white paint?
4. can the sum of three consecutive odd integers be (a) 25? (b) 45?
5. a tank can be filled in 9 hours by one pipe alone, in 12 hours by a second pipe alone, and can be drained when full, by a third pipe, in 15 hours. how long would it take to fill the tank if it is empty, and if all pipes are in operations?

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.