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Finding the Third Proportional to 309,314 and 470,451

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Solution

The third proportional to 309,314 and 470,451 is: 715,532.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    309,314 : 470,451 = 470,451 : x
  2. Step 2: Convert to fraction form
    309,314/470,451 = 470,451/x
  3. Step 3: Cross multiply
    309,314x = 470,451 × 470,451
  4. Step 4: Simplify right side
    309,314x = 221,324,143,401
  5. Step 5: Solve for x
    x = 221,324,143,401/309,314
  6. Step 6: Final answer
    x = 715,532.25

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.