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Finding the Third Proportional to 19,730 and 41,971

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Solution

The third proportional to 19,730 and 41,971 is: 89,283.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,730 : 41,971 = 41,971 : x
  2. Step 2: Convert to fraction form
    19,730/41,971 = 41,971/x
  3. Step 3: Cross multiply
    19,730x = 41,971 × 41,971
  4. Step 4: Simplify right side
    19,730x = 1,761,564,841
  5. Step 5: Solve for x
    x = 1,761,564,841/19,730
  6. Step 6: Final answer
    x = 89,283.57

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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.