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Finding the Third Proportional to 214.78 and 464.16

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Solution

The third proportional to 214.78 and 464.16 is: 1,003.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.78 : 464.16 = 464.16 : x
  2. Step 2: Convert to fraction form
    214.78/464.16 = 464.16/x
  3. Step 3: Cross multiply
    214.78x = 464.16 × 464.16
  4. Step 4: Simplify right side
    214.78x = 215,441.02
  5. Step 5: Solve for x
    x = 215,441.02/214.78
  6. Step 6: Final answer
    x = 1,003.07

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.