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. How many cans are there per pound of aluminum?
The correct answer and explanation is:
To find the number of cans required per pound of aluminum, we start with the given information:
- 8 empty cans make 14\frac{1}{4} pound of aluminum.
Step 1: Determine how many cans make 1 pound
Since 8 cans make 14\frac{1}{4} pound, we need to determine how many such groups make 1 pound: Cans per pound=8×4=32\text{Cans per pound} = 8 \times 4 = 32
Thus, 32 cans are needed to make 1 pound of aluminum.
Step 2: Find how many cans make 5 pounds
Now, to determine how many cans are required for 5 pounds of aluminum, we multiply: 5×32=1605 \times 32 = 160
So, Shyla needs 160 cans to make 5 pounds of aluminum.
Explanation:
This problem is a straightforward proportion-based calculation. Given that 8 cans make 14\frac{1}{4} pound, we realize that one full pound contains four times that amount. Thus, we multiply the number of cans required for 14\frac{1}{4} pound by 4 to get the number of cans per full pound. Once we have the cans per pound (32), we can easily scale this to any number of pounds by simple multiplication.
This method is useful in real-life applications such as recycling programs, where knowing how much aluminum is recovered from cans helps in estimating costs and environmental impacts.
Now, I will generate an image to visually represent this concept.
The image visually represents the concept by showing aluminum cans on a scale, with clear labels for different weight measurements (1/4 pound, 1 pound, and 5 pounds). Let me know if you need any modifications or further explanations!
