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Finding the Third Proportional to 640 and 1,402

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Solution

The third proportional to 640 and 1,402 is: 3,071.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    640 : 1,402 = 1,402 : x
  2. Step 2: Convert to fraction form
    640/1,402 = 1,402/x
  3. Step 3: Cross multiply
    640x = 1,402 × 1,402
  4. Step 4: Simplify right side
    640x = 1,965,604
  5. Step 5: Solve for x
    x = 1,965,604/640
  6. Step 6: Final answer
    x = 3,071.26

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.