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Finding the Third Proportional to 1,416 and 1,906

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Solution

The third proportional to 1,416 and 1,906 is: 2,565.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,416 : 1,906 = 1,906 : x
  2. Step 2: Convert to fraction form
    1,416/1,906 = 1,906/x
  3. Step 3: Cross multiply
    1,416x = 1,906 × 1,906
  4. Step 4: Simplify right side
    1,416x = 3,632,836
  5. Step 5: Solve for x
    x = 3,632,836/1,416
  6. Step 6: Final answer
    x = 2,565.56

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.