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Finding the Third Proportional to 684 and 1,854

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Solution

The third proportional to 684 and 1,854 is: 5,025.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    684 : 1,854 = 1,854 : x
  2. Step 2: Convert to fraction form
    684/1,854 = 1,854/x
  3. Step 3: Cross multiply
    684x = 1,854 × 1,854
  4. Step 4: Simplify right side
    684x = 3,437,316
  5. Step 5: Solve for x
    x = 3,437,316/684
  6. Step 6: Final answer
    x = 5,025.32

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Why These Related Problems?

These problems maintain the same ratio (2.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.