Henry bought 5/6 pound of roasted almonds for five dollars. He wants to know the price per pound.
The correct answer and explanation is:
Answer: The price per pound of the roasted almonds is $6.
Explanation:
Henry bought 5/6 of a pound of roasted almonds for 5 dollars. To find the price per pound, we want to know how much 1 full pound of almonds would cost, assuming the price per pound is consistent.
This is a typical unit rate problem where you have a quantity (weight) and a total cost, and you want to find the cost for a standard unit (1 pound).
Step-by-step solution:
- Identify the quantities:
- Amount bought: 56\frac{5}{6} pounds
- Total cost: $5
- Price per pound: unknown (let’s call it pp)
- Set up the relationship: If pp is the price per pound, then the cost for 56\frac{5}{6} pounds is: Cost=weight×price per pound=56×p\text{Cost} = \text{weight} \times \text{price per pound} = \frac{5}{6} \times p
- Use the given cost: The cost for 56\frac{5}{6} pounds is $5, so: 56×p=5\frac{5}{6} \times p = 5
- Solve for pp: Multiply both sides by 65\frac{6}{5} to isolate pp: p=5×65=6p = 5 \times \frac{6}{5} = 6
Interpretation:
- The price per pound is $6.
- That means if Henry wanted to buy exactly 1 pound of these roasted almonds, it would cost him 6 dollars.
- Since he bought less than a pound (5/6 of a pound), the total cost was correspondingly less ($5).
Additional notes:
- This kind of problem helps understand unit rates, which is a fundamental concept in proportional reasoning.
- It’s common in shopping, cooking, and many real-world scenarios to convert prices or quantities to a per-unit basis to compare prices or understand costs better.
- You can always check your answer by multiplying the price per pound by the fraction of the pound bought:
6×56=56 \times \frac{5}{6} = 5
which matches the given total cost.