Final answer:
The weight of rice needed to fill one container is found by setting up a proportion where (3/4 pounds) / (2/5 container) = (x pounds) / (1 container), which results in 1 and 7/8 pounds of rice to fill the entire container.
Step-by-step explanation:
The question involves using proportional reasoning to determine how many pounds of rice would fill one container if 3/4 pounds of rice fills 2/5 of a container. We set up a proportion to solve for the total weight needed to fill one container. Since we know that 16 ounces equates to one pound, converting between ounces and pounds could be necessary to understand weight comparisons or conversions in other problems.
To find the weight that fills one container, we start with the given proportion: 3/4 pounds fills 2/5 of a container. Since we want to find the weight that fills one whole container (5/5), we setup the proportion like this:
- (3/4 pounds) / (2/5 container) = (x pounds) / (1 container)
By cross multiplying, we get:
To solve for x, we multiply both sides by the reciprocal of (2/5) which is (5/2):
Therefore, x = (3/4) * (5/2) = 15/8 pounds. This simplifies to 1 and 7/8 pounds.