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Finding the Third Proportional to 322.10 and 689.77

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Solution

The third proportional to 322.10 and 689.77 is: 1,477.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    322.10 : 689.77 = 689.77 : x
  2. Step 2: Convert to fraction form
    322.10/689.77 = 689.77/x
  3. Step 3: Cross multiply
    322.10x = 689.77 × 689.77
  4. Step 4: Simplify right side
    322.10x = 475,776.62
  5. Step 5: Solve for x
    x = 475,776.62/322.10
  6. Step 6: Final answer
    x = 1,477.10

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.