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Finding the Third Proportional to 212,949 and 470,205

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Solution

The third proportional to 212,949 and 470,205 is: 1,038,242.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,949 : 470,205 = 470,205 : x
  2. Step 2: Convert to fraction form
    212,949/470,205 = 470,205/x
  3. Step 3: Cross multiply
    212,949x = 470,205 × 470,205
  4. Step 4: Simplify right side
    212,949x = 221,092,742,025
  5. Step 5: Solve for x
    x = 221,092,742,025/212,949
  6. Step 6: Final answer
    x = 1,038,242.69

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.