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Finding the Third Proportional to 414.84 and 1,030.78

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Solution

The third proportional to 414.84 and 1,030.78 is: 2,561.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.84 : 1,030.78 = 1,030.78 : x
  2. Step 2: Convert to fraction form
    414.84/1,030.78 = 1,030.78/x
  3. Step 3: Cross multiply
    414.84x = 1,030.78 × 1,030.78
  4. Step 4: Simplify right side
    414.84x = 1,062,509.99
  5. Step 5: Solve for x
    x = 1,062,509.99/414.84
  6. Step 6: Final answer
    x = 2,561.23

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.