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Finding the Third Proportional to 5,709 and 9,146

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Solution

The third proportional to 5,709 and 9,146 is: 14,652.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,709 : 9,146 = 9,146 : x
  2. Step 2: Convert to fraction form
    5,709/9,146 = 9,146/x
  3. Step 3: Cross multiply
    5,709x = 9,146 × 9,146
  4. Step 4: Simplify right side
    5,709x = 83,649,316
  5. Step 5: Solve for x
    x = 83,649,316/5,709
  6. Step 6: Final answer
    x = 14,652.18

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.