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Finding the Third Proportional to 315,840 and 463,968

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Solution

The third proportional to 315,840 and 463,968 is: 681,567.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    315,840 : 463,968 = 463,968 : x
  2. Step 2: Convert to fraction form
    315,840/463,968 = 463,968/x
  3. Step 3: Cross multiply
    315,840x = 463,968 × 463,968
  4. Step 4: Simplify right side
    315,840x = 215,266,305,024
  5. Step 5: Solve for x
    x = 215,266,305,024/315,840
  6. Step 6: Final answer
    x = 681,567.58

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.