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Finding the Third Proportional to 407.74 and 828.77

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Solution

The third proportional to 407.74 and 828.77 is: 1,684.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    407.74 : 828.77 = 828.77 : x
  2. Step 2: Convert to fraction form
    407.74/828.77 = 828.77/x
  3. Step 3: Cross multiply
    407.74x = 828.77 × 828.77
  4. Step 4: Simplify right side
    407.74x = 686,865.41
  5. Step 5: Solve for x
    x = 686,865.41/407.74
  6. Step 6: Final answer
    x = 1,684.56

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.