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Finding the Third Proportional to 657.50 and 1,022.63

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Solution

The third proportional to 657.50 and 1,022.63 is: 1,590.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    657.50 : 1,022.63 = 1,022.63 : x
  2. Step 2: Convert to fraction form
    657.50/1,022.63 = 1,022.63/x
  3. Step 3: Cross multiply
    657.50x = 1,022.63 × 1,022.63
  4. Step 4: Simplify right side
    657.50x = 1,045,761.89
  5. Step 5: Solve for x
    x = 1,045,761.89/657.50
  6. Step 6: Final answer
    x = 1,590.51

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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.