Questions: Ari mixed 2 1/4 cups of red grapes with 1/2 cups of green grapes. He then divided the grapes into bags with 3/4 cup of mixed grapes in each. How many bags of grapes will Ari have?

Solution Steps

To find out how many bags of grapes Ari will have, we need to first determine the total amount of grapes by adding the cups of red and green grapes. Then, we divide the total amount of grapes by the amount of grapes per bag to find the number of bags.

We start by calculating the total amount of grapes mixed by Ari. The amount of red grapes is given as $2 \frac{1}{4}$ cups, which can be expressed as: $$2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{9}{4}$$ The amount of green grapes is $\frac{1}{2}$ cups. Therefore, the total amount of grapes is: $$\text{Total Grapes} = \frac{9}{4} + \frac{1}{2} = \frac{9}{4} + \frac{2}{4} = \frac{11}{4}$$

Ari divides the total grapes into bags, with each bag containing $\frac{3}{4}$ cup of mixed grapes.

To find the number of bags, we divide the total amount of grapes by the amount of grapes per bag: $$\text{Number of Bags} = \frac{\text{Total Grapes}}{\text{Grapes per Bag}} = \frac{\frac{11}{4}}{\frac{3}{4}} = \frac{11}{4} \times \frac{4}{3} = \frac{11}{3} \approx 3.6667$$

Final Answer