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Finding the Third Proportional to 413,329 and 585,021

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Solution

The third proportional to 413,329 and 585,021 is: 828,031.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,329 : 585,021 = 585,021 : x
  2. Step 2: Convert to fraction form
    413,329/585,021 = 585,021/x
  3. Step 3: Cross multiply
    413,329x = 585,021 × 585,021
  4. Step 4: Simplify right side
    413,329x = 342,249,570,441
  5. Step 5: Solve for x
    x = 342,249,570,441/413,329
  6. Step 6: Final answer
    x = 828,031.84

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.