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Finding the Third Proportional to 413,342 and 585,041

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Solution

The third proportional to 413,342 and 585,041 is: 828,062.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    413,342 : 585,041 = 585,041 : x
  2. Step 2: Convert to fraction form
    413,342/585,041 = 585,041/x
  3. Step 3: Cross multiply
    413,342x = 585,041 × 585,041
  4. Step 4: Simplify right side
    413,342x = 342,272,971,681
  5. Step 5: Solve for x
    x = 342,272,971,681/413,342
  6. Step 6: Final answer
    x = 828,062.41

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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.