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Finding the Third Proportional to 642 and 709.50

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Solution

The third proportional to 642 and 709.50 is: 784.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    642 : 709.50 = 709.50 : x
  2. Step 2: Convert to fraction form
    642/709.50 = 709.50/x
  3. Step 3: Cross multiply
    642x = 709.50 × 709.50
  4. Step 4: Simplify right side
    642x = 503,390.25
  5. Step 5: Solve for x
    x = 503,390.25/642
  6. Step 6: Final answer
    x = 784.10

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.