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Finding the Third Proportional to 415.31 and 689.06

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Solution

The third proportional to 415.31 and 689.06 is: 1,143.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.31 : 689.06 = 689.06 : x
  2. Step 2: Convert to fraction form
    415.31/689.06 = 689.06/x
  3. Step 3: Cross multiply
    415.31x = 689.06 × 689.06
  4. Step 4: Simplify right side
    415.31x = 474,807.13
  5. Step 5: Solve for x
    x = 474,807.13/415.31
  6. Step 6: Final answer
    x = 1,143.25

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.