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Difficulty: MediumWeighted Average and Combined Sets

A real estate developer purchased two tracts of land. Tract 1 consists of 1515 acres purchased at an average cost of $24,000\$24,000 per acre. Tract 2 consists of 3535 acres purchased at an average cost of $40,000\$40,000 per acre. What is the average cost per acre, in thousands of dollars, for the combined land purchase?

Answer: 35.2 thousand dollars

Answer

The average cost per acre for the combined land purchase is 35.235.2 thousand dollars (or $35,200\$35,200).
The overall weighted average is calculated by dividing the sum of all individual costs by the total number of acres across both tracts. Since 1515 acres cost $24,000\$24,000 per acre and 3535 acres cost $40,000\$40,000 per acre, the total cost is 15(24,000)+35(40,000)=360,000+1,400,000=1,760,00015(24,000) + 35(40,000) = 360,000 + 1,400,000 = 1,760,000 dollars. Dividing by the total of 5050 acres yields $35,200\$35,200 per acre, or 35.235.2 thousand dollars.

Step-by-Step Solution

1
Determine the total financial expenditure for each tract
Tract 1 cost = 15×24,000=$360,00015 \times 24,000 = \$360,000; Tract 2 cost = 35×40,000=$1,400,00035 \times 40,000 = \$1,400,000
Total value of a set equals the number of items multiplied by the mean of the items.
2
Calculate total combined cost and total combined acreage
Total cost = $360,000+$1,400,000=$1,760,000\$360,000 + \$1,400,000 = \$1,760,000; Total acres = 15+35=5015 + 35 = 50
Combined sets require summing all total values and all individual counts.
3
Compute the weighted average cost per acre
Weighted Mean = 1,760,00050=35,200\frac{1,760,000}{50} = 35,200 dollars, which is 35.235.2 thousand dollars.
Divide total combined cost by total combined number of units.

Key Concept

Weighted Average of Combined Sets
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Topics

Weighted Average and Combined Sets

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