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Finding the Third Proportional to 5,946 and 9,205

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Solution

The third proportional to 5,946 and 9,205 is: 14,250.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,946 : 9,205 = 9,205 : x
  2. Step 2: Convert to fraction form
    5,946/9,205 = 9,205/x
  3. Step 3: Cross multiply
    5,946x = 9,205 × 9,205
  4. Step 4: Simplify right side
    5,946x = 84,732,025
  5. Step 5: Solve for x
    x = 84,732,025/5,946
  6. Step 6: Final answer
    x = 14,250.26

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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.