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Finding the Third Proportional to 4,114 and 5,659

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Solution

The third proportional to 4,114 and 5,659 is: 7,784.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,114 : 5,659 = 5,659 : x
  2. Step 2: Convert to fraction form
    4,114/5,659 = 5,659/x
  3. Step 3: Cross multiply
    4,114x = 5,659 × 5,659
  4. Step 4: Simplify right side
    4,114x = 32,024,281
  5. Step 5: Solve for x
    x = 32,024,281/4,114
  6. Step 6: Final answer
    x = 7,784.22

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.