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Finding the Third Proportional to 780 and 2,054

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Solution

The third proportional to 780 and 2,054 is: 5,408.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    780 : 2,054 = 2,054 : x
  2. Step 2: Convert to fraction form
    780/2,054 = 2,054/x
  3. Step 3: Cross multiply
    780x = 2,054 × 2,054
  4. Step 4: Simplify right side
    780x = 4,218,916
  5. Step 5: Solve for x
    x = 4,218,916/780
  6. Step 6: Final answer
    x = 5,408.87

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Why These Related Problems?

These problems maintain the same ratio (2.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.