Question: In October, the average price of aluminum was 75 1/2¢ per pound. During that time, Severo received 906¢ for aluminum cans that he sold for recycling at a scrap metal center. Assuming that he received the average price, how many pounds of aluminum cans did Severo recycle?
Severo recycled ☐ pounds of aluminum cans. (Type a whole number or a simplified fraction.)
1. **State the problem:** We need to find how many pounds of aluminum cans Severo recycled if he received 906¢ and the average price was 75 1/2¢ per pound.
2. **Convert mixed number to improper fraction:** The price per pound is 75 1/2¢, which is $$75 \frac{1}{2} = \frac{151}{2}$$ cents per pound.
3. **Set up the equation:** Let $x$ be the pounds of aluminum recycled. Then,
$$\text{price per pound} \times \text{pounds} = \text{total cents received}$$
$$\frac{151}{2} \times x = 906$$
4. **Solve for $x$:**
$$x = \frac{906}{\frac{151}{2}} = 906 \times \frac{2}{151}$$
5. **Simplify the multiplication:**
$$x = \frac{906 \times 2}{151} = \frac{1812}{151}$$
6. **Check for simplification:**
151 is a prime number and does not divide 1812 evenly, so the fraction is already simplified.
7. **Convert to mixed number:**
Divide 1812 by 151:
$$151 \times 12 = 1812$$
So,
$$x = 12$$
**Final answer:** Severo recycled $$12$$ pounds of aluminum cans.