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Finding the Third Proportional to 708 and 778.50

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Solution

The third proportional to 708 and 778.50 is: 856.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    708 : 778.50 = 778.50 : x
  2. Step 2: Convert to fraction form
    708/778.50 = 778.50/x
  3. Step 3: Cross multiply
    708x = 778.50 × 778.50
  4. Step 4: Simplify right side
    708x = 606,062.25
  5. Step 5: Solve for x
    x = 606,062.25/708
  6. Step 6: Final answer
    x = 856.02

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.