Short Answer 
To produce 5 lbs, 160 cans are needed, while 32 cans are required for 1 lb, based on the established ratio of 8 cans for 1/4 lb.
Step 1: Understand the Ratios
To determine how many cans are required, we start by analyzing the provided ratios. We know that 8 cans correspond to 1/4 lbs. This means we can establish a proportional relationship between cans and pounds of product. The overall goal is to scale this ratio to find out how many cans are needed for larger quantities.
Step 2: Set Up the Proportions
We can form the ratio as follows: 8 cans / (1/4 lbs) = x cans / 5 lbs. By using cross multiplication, we solve for x to find the total number of cans needed for 5 lbs. The steps are:
- Cross multiply: 8 * 5 = (1/4) * x
- Multiply both sides by 4 to isolate x: 32 * 40 = x
- Which results in: x = 160 cans
Step 3: Calculate Cans Needed for 1 lb
Next, we simplify to find out how many cans are needed for just 1 pound. We can use the same initial ratio, simplifying it to 8 cans / (1/4 lbs) = x cans / 1 lb. The process follows similar steps:
- Cross multiply: 8 * 1 = (1/4) * x
- Again, multiply both sides by 4: 32 = x
This means you will need 32 cans to produce 1 lb.