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Finding the Third Proportional to 257,752 and 409,020

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Solution

The third proportional to 257,752 and 409,020 is: 649,063.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,752 : 409,020 = 409,020 : x
  2. Step 2: Convert to fraction form
    257,752/409,020 = 409,020/x
  3. Step 3: Cross multiply
    257,752x = 409,020 × 409,020
  4. Step 4: Simplify right side
    257,752x = 167,297,360,400
  5. Step 5: Solve for x
    x = 167,297,360,400/257,752
  6. Step 6: Final answer
    x = 649,063.29

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.