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Finding the Third Proportional to 212,969 and 470,224

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Solution

The third proportional to 212,969 and 470,224 is: 1,038,229.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    212,969 : 470,224 = 470,224 : x
  2. Step 2: Convert to fraction form
    212,969/470,224 = 470,224/x
  3. Step 3: Cross multiply
    212,969x = 470,224 × 470,224
  4. Step 4: Simplify right side
    212,969x = 221,110,610,176
  5. Step 5: Solve for x
    x = 221,110,610,176/212,969
  6. Step 6: Final answer
    x = 1,038,229.09

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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.