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Finding the Third Proportional to 586 and 1,417

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Solution

The third proportional to 586 and 1,417 is: 3,426.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    586 : 1,417 = 1,417 : x
  2. Step 2: Convert to fraction form
    586/1,417 = 1,417/x
  3. Step 3: Cross multiply
    586x = 1,417 × 1,417
  4. Step 4: Simplify right side
    586x = 2,007,889
  5. Step 5: Solve for x
    x = 2,007,889/586
  6. Step 6: Final answer
    x = 3,426.43

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.