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Finding the Third Proportional to 301,291 and 413,142

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Solution

The third proportional to 301,291 and 413,142 is: 566,516.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    301,291 : 413,142 = 413,142 : x
  2. Step 2: Convert to fraction form
    301,291/413,142 = 413,142/x
  3. Step 3: Cross multiply
    301,291x = 413,142 × 413,142
  4. Step 4: Simplify right side
    301,291x = 170,686,312,164
  5. Step 5: Solve for x
    x = 170,686,312,164/301,291
  6. Step 6: Final answer
    x = 566,516.46

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.