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Finding the Third Proportional to 311,976 and 470,772

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Solution

The third proportional to 311,976 and 470,772 is: 710,395.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,976 : 470,772 = 470,772 : x
  2. Step 2: Convert to fraction form
    311,976/470,772 = 470,772/x
  3. Step 3: Cross multiply
    311,976x = 470,772 × 470,772
  4. Step 4: Simplify right side
    311,976x = 221,626,275,984
  5. Step 5: Solve for x
    x = 221,626,275,984/311,976
  6. Step 6: Final answer
    x = 710,395.27

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.