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Finding the Third Proportional to 463 and 689.50

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Solution

The third proportional to 463 and 689.50 is: 1,026.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    463 : 689.50 = 689.50 : x
  2. Step 2: Convert to fraction form
    463/689.50 = 689.50/x
  3. Step 3: Cross multiply
    463x = 689.50 × 689.50
  4. Step 4: Simplify right side
    463x = 475,410.25
  5. Step 5: Solve for x
    x = 475,410.25/463
  6. Step 6: Final answer
    x = 1,026.80

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.