Shyla’s research shows that 8 empty cans make 1/4
pound of aluminum. Shyla wants to know how many cans it takes to make 5 pounds of aluminum
The Correct Answer and Explanation is:
To determine how many cans are needed to make 5 pounds of aluminum, we start by analyzing the information given:
- 8 empty cans make ¼ pound of aluminum.
We need to find out how many cans will make 5 pounds.
Step 1: Determine how many ¼ pounds are in 5 pounds.
Since 1 pound contains 4 quarters (¼):5 pounds=5×4=20 quarters (¼ pounds)5 \text{ pounds} = 5 \times 4 = 20 \text{ quarters (¼ pounds)}5 pounds=5×4=20 quarters (¼ pounds)
Step 2: Determine how many cans are needed for 20 quarters.
If 8 cans make ¼ pound, then for 20 quarters:20×8=160 cans20 \times 8 = 160 \text{ cans}20×8=160 cans
✅ Final Answer: 160 cans
Explanation:
To solve this problem, we use proportional reasoning. Shyla’s research tells us that 8 empty aluminum cans yield ¼ pound of aluminum. This means that every ¼ pound requires 8 cans. Her goal is to find out how many cans are needed to obtain 5 full pounds.
First, we convert 5 pounds into a number of quarter-pounds, since we know the can-to-weight ratio in quarters. Since each pound is made up of four quarters, multiplying 5 pounds by 4 gives us 20 quarters (5 × 4 = 20). This step is crucial because the ratio we have—8 cans per ¼ pound—needs to be scaled up to match the larger amount of aluminum (5 pounds).
Next, we scale up the number of cans accordingly. If 8 cans produce ¼ pound, then to produce 20 such quarters, we multiply 8 by 20. This gives us 160 cans (8 × 20 = 160). That means it takes 160 empty aluminum cans to make 5 pounds of aluminum.
This method works because the relationship between cans and aluminum is linear and consistent—each additional ¼ pound always requires 8 more cans. Therefore, proportional multiplication provides an accurate and logical way to scale from a smaller unit (¼ pound) to a larger total (5 pounds).
Understanding this kind of ratio and unit conversion is a key math skill, especially useful in real-world scenarios like recycling, budgeting, or any case where small measurements must be scaled.
