# 6.2.4. Proportional Division

A man passed away and left behind a piece of land having an area of 80 acres. In his will, he stated that an orphanage is to be built on a part of the land and the remainder is to be distributed between his son and daughter with a ratio of . Given that the area of the orphanage is 8 acres, determine the shares of both the son and the daughter.

• A son's share acres, daughter's share acres
• B son's share acres, daughter's share acres
• C son's share acres, daughter's share acres
• D son's share acres, daughter's share acres

### Example

A man passed away and left behind a piece of land having an area of 80 acres. In his will, he stated that an orphanage is to be built on a part of the land and the remainder is to be distributed between his son and daughter with a ratio of . Given that the area of the orphanage is 8 acres, determine the shares of both the son and the daughter.

### Solution

Step 1: Determine the amount of land that is to be distributed to the son and daughter.

Subtract the area of the orphanage from the total area.

Step 2: Use the concept of "the sum of parts" to show how to distribute the land.

The son's share of the land acres.

The daughter's share of the land acres.

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