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Finding the Third Proportional to 5,034 and 7,780

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Solution

The third proportional to 5,034 and 7,780 is: 12,023.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,034 : 7,780 = 7,780 : x
  2. Step 2: Convert to fraction form
    5,034/7,780 = 7,780/x
  3. Step 3: Cross multiply
    5,034x = 7,780 × 7,780
  4. Step 4: Simplify right side
    5,034x = 60,528,400
  5. Step 5: Solve for x
    x = 60,528,400/5,034
  6. Step 6: Final answer
    x = 12,023.92

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.