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Difficulty: EasyWeighted Averages in Applied Contexts

A merchant combines 1010 kilograms of Brand A tea costing $20\$20 per kilogram with 3030 kilograms of Brand B tea costing $40\$40 per kilogram. What is the average cost per kilogram of the combined mixture?

  1. A
    $30\$30
  2. $35\$35Answer
  3. C
    $25\$25
  4. D
    $28\$28
  5. E
    $60\$60

Answer

The average cost per kilogram of the combined tea mixture is $35\$35.
The correct option of $35\$35 properly weights each unit price by its respective quantity. Brand A contributes 10×20=$20010 \times 20 = \$200 and Brand B contributes 30×40=$120030 \times 40 = \$1200, giving a combined total cost of $1400\$1400 for 4040 kg. Dividing $1400\$1400 by 4040 yields $35\$35 per kilogram.

Step-by-Step Solution

1
Calculate the total cost of Brand A tea
10 kg×$20/kg=$20010 \text{ kg} \times \$20/\text{kg} = \$200
To find the overall weighted cost, we first determine the total dollar amount spent on Brand A.
2
Calculate the total cost of Brand B tea
30 kg×$40/kg=$120030 \text{ kg} \times \$40/\text{kg} = \$1200
Next, we calculate the total dollar amount spent on Brand B.
3
Find total combined cost and total combined weight
\text{Total cost} = \$200 + \$1200 = \$1400; \text{Total weight} = 10 + 30 = 40 \text{ kg}
Sum the total cost of both components and their combined weights.
4
Divide total combined cost by total combined weight
\text{Weighted Average Cost} = \frac{\$1400}{40 \text{ kg}} = \$35/\text{kg}
The weighted average formula is Total Cost divided by Total Quantity.

Key Concept

Weighted Average in Applied Contexts
Estimated Time:1m 0s
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Topics

Weighted Averages in Applied Contexts

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