Given that her lasagna recipe calls for 1 1/4 = 5/4 cups of tomato paste and that she will double her lasagna recipe, then the number of cups of tomato paste she will use in making double lasagna recipe is given by 2(5/4) = 10/4 = 5/2.
Given that her pizza recipe uses 1/2 cup of tomato paste per pizza and that she will make 5 pizzas, then the number of cups of tomato paste she will use in making 5 pizzas is given by 5(1/2) = 5/2.
The total number of cups of tomato paste she will use in making double lasagna and 5 pizzas is given by 5/2 + 5/2 = 5 cups.
Therefore, the number of 3/4 - cup cans of tomato paste she will need in all is given by 5/(3/4) = (5 x 4)/3 = 20/3 = 6 2/3.