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Difficulty: HardUnit Price Comparisons

A military mess hall requires exactly 500500 pounds of flour. Supplier A sells flour in 2525-pound bags for $14.00\$14.00 per bag. Supplier B sells the same flour in 4040-ounce boxes for $1.50\$1.50 per box. How much total money, in dollars, is saved by purchasing the entire 500500 pounds from the more cost-effective supplier instead of the less cost-effective one?

Answer: 20 dollars

Answer

The savings amount to 20 dollars.
Supplier A's total cost for 500 pounds is 280(20bags×280 (20 bags × 14.00), and Supplier B's total cost is 300(200boxes×300 (200 boxes × 1.50). Purchasing from Supplier A saves $20.

Step-by-Step Solution

1
Convert the weight of Supplier B's boxes from ounces to pounds.
4040 ounces ÷16\div 16 ounces/pound = 2.52.5 pounds per box.
Measurements must be in the same unit (pounds) to accurately calculate the required number of packages and compare costs.
2
Determine the number of packages required from each supplier to get exactly 500 pounds.
Supplier A: 500÷25=20500 \div 25 = 20 bags. Supplier B: 500÷2.5=200500 \div 2.5 = 200 boxes.
This establishes the exact purchasing volume needed for the final cost calculation.
3
Calculate the total cost for each supplier.
Supplier A: 2020 bags ×$14.00\times \$14.00 = $280\$280. Supplier B: 200200 boxes ×$1.50\times \$1.50 = $300\$300.
Total cost is the package count multiplied by the price per package.
4
Calculate the difference between the two total costs.
$300−$280=$20\$300 - \$280 = \$20.
Subtracting the most cost-effective option from the alternative gives the total savings.

Key Concept

Calculating and comparing total costs across different measurement units by determining unit prices and required volumes.

Alternative Method

Instead of computing total costs, calculate the unit price per pound for both. Supplier A: $14.00÷25=$0.56\$14.00 \div 25 = \$0.56 per pound. Supplier B: 4040 oz is 2.52.5 lbs; $1.50÷2.5=$0.60\$1.50 \div 2.5 = \$0.60 per pound. The difference is $0.04\$0.04 per pound. Multiply this difference by the 500500 pounds needed: 500×$0.04=$20500 \times \$0.04 = \$20.
Estimated Time:2m 30s
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