A box of 6 trophies costs 5$. How much would it cost to buy 48 trophies
The Correct Answer and Explanation is:
To find the cost of 48 trophies when a box of 6 trophies costs $5, we first determine how many boxes are needed: Number of boxes=486=8\text{Number of boxes} = \frac{48}{6} = 8
Now, if each box costs $5: Total cost=8×5=40 dollars\text{Total cost} = 8 \times 5 = \boxed{40\text{ dollars}}
Explanation
To determine the cost of 48 trophies, we begin by understanding the relationship between quantity and cost. According to the given information, a box that contains 6 trophies costs $5. This means the cost is not provided per individual trophy but per group of 6.
To find how many such boxes are needed to get 48 trophies, we divide 48 by 6: 48÷6=848 \div 6 = 8
This means we need 8 boxes to have a total of 48 trophies.
Since each box costs $5, we then multiply the number of boxes by the price per box: 8×5=408 \times 5 = 40
Therefore, the total cost for 48 trophies is $40.
This approach uses a basic concept of unit pricing and multiplication. It’s important to recognize that when quantities are bundled—like trophies sold in boxes—we must first determine how many such bundles are required. If we had mistakenly tried to find the cost per trophy first, we could divide $5 by 6, getting approximately $0.8333 per trophy, and then multiply that by 48: 48×0.8333≈4048 \times 0.8333 \approx 40
While this gives a similar result (due to rounding), using the box-based approach is more accurate and straightforward in this context.
Understanding how to scale costs from small groupings to larger quantities is a foundational math skill, especially in budgeting and purchasing scenarios. It ensures precision, especially when dealing with fixed-unit packaging, and helps avoid errors that might arise from rounding decimal values. Thus, the total cost of 48 trophies is correctly and clearly $40.
