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Finding the Third Proportional to 509 and 778

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Solution

The third proportional to 509 and 778 is: 1,189.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 778 = 778 : x
  2. Step 2: Convert to fraction form
    509/778 = 778/x
  3. Step 3: Cross multiply
    509x = 778 × 778
  4. Step 4: Simplify right side
    509x = 605,284
  5. Step 5: Solve for x
    x = 605,284/509
  6. Step 6: Final answer
    x = 1,189.16

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.