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Finding the Third Proportional to 657.49 and 1,023.57

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Solution

The third proportional to 657.49 and 1,023.57 is: 1,593.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    657.49 : 1,023.57 = 1,023.57 : x
  2. Step 2: Convert to fraction form
    657.49/1,023.57 = 1,023.57/x
  3. Step 3: Cross multiply
    657.49x = 1,023.57 × 1,023.57
  4. Step 4: Simplify right side
    657.49x = 1,047,704.18
  5. Step 5: Solve for x
    x = 1,047,704.18/657.49
  6. Step 6: Final answer
    x = 1,593.49

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.