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Finding the Third Proportional to 53,411 and 113,971

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Solution

The third proportional to 53,411 and 113,971 is: 243,196.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,411 : 113,971 = 113,971 : x
  2. Step 2: Convert to fraction form
    53,411/113,971 = 113,971/x
  3. Step 3: Cross multiply
    53,411x = 113,971 × 113,971
  4. Step 4: Simplify right side
    53,411x = 12,989,388,841
  5. Step 5: Solve for x
    x = 12,989,388,841/53,411
  6. Step 6: Final answer
    x = 243,196.89

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.