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Finding the Third Proportional to 312,012 and 470,223

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Solution

The third proportional to 312,012 and 470,223 is: 708,657.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    312,012 : 470,223 = 470,223 : x
  2. Step 2: Convert to fraction form
    312,012/470,223 = 470,223/x
  3. Step 3: Cross multiply
    312,012x = 470,223 × 470,223
  4. Step 4: Simplify right side
    312,012x = 221,109,669,729
  5. Step 5: Solve for x
    x = 221,109,669,729/312,012
  6. Step 6: Final answer
    x = 708,657.58

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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.