If 5 pounds of beans cost $4, then how much does 50 pounds of beans cost?
The correct answer and explanation is:
Correct Answer: $40
Explanation:
To determine how much 50 pounds of beans cost if 5 pounds cost $4, we can use a unit rate and apply proportional reasoning.
Step-by-Step Method:
- Find the cost per pound: Cost per pound=$45 pounds=$0.80 per pound\text{Cost per pound} = \frac{\$4}{5 \text{ pounds}} = \$0.80 \text{ per pound}
- Multiply the cost per pound by 50: Cost of 50 pounds=50×0.80=$40\text{Cost of 50 pounds} = 50 \times 0.80 = \$40
Alternative Proportion Method:
We can also solve this using a proportion:
Let xx be the cost of 50 pounds. 5$4=50x\frac{5}{\$4} = \frac{50}{x}
Cross-multiply: 5x=4×50=2005x = 4 \times 50 = 200 x=2005=$40x = \frac{200}{5} = \$40
Why It Works:
This problem involves direct proportionality. When two quantities (like weight and cost) increase at the same rate, their ratio remains constant. In this case, the price increases at a steady rate of $0.80 per pound. So, multiplying the cost per unit by the number of units gives the total cost.
This concept is important in everyday life when budgeting or comparing prices, whether shopping for groceries, buying materials, or calculating expenses.
By understanding unit rates and proportional reasoning, you can solve a wide variety of similar real-world math problems with confidence.
Final Answer: $40