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Finding the Third Proportional to 785 and 1,457

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Solution

The third proportional to 785 and 1,457 is: 2,704.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    785 : 1,457 = 1,457 : x
  2. Step 2: Convert to fraction form
    785/1,457 = 1,457/x
  3. Step 3: Cross multiply
    785x = 1,457 × 1,457
  4. Step 4: Simplify right side
    785x = 2,122,849
  5. Step 5: Solve for x
    x = 2,122,849/785
  6. Step 6: Final answer
    x = 2,704.27

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.