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Finding the Third Proportional to 398.14 and 824.24

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Solution

The third proportional to 398.14 and 824.24 is: 1,706.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    398.14 : 824.24 = 824.24 : x
  2. Step 2: Convert to fraction form
    398.14/824.24 = 824.24/x
  3. Step 3: Cross multiply
    398.14x = 824.24 × 824.24
  4. Step 4: Simplify right side
    398.14x = 679,368.74
  5. Step 5: Solve for x
    x = 679,368.74/398.14
  6. Step 6: Final answer
    x = 1,706.34

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.