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Finding the Third Proportional to 9,738 and 14,971

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Solution

The third proportional to 9,738 and 14,971 is: 23,016.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,738 : 14,971 = 14,971 : x
  2. Step 2: Convert to fraction form
    9,738/14,971 = 14,971/x
  3. Step 3: Cross multiply
    9,738x = 14,971 × 14,971
  4. Step 4: Simplify right side
    9,738x = 224,130,841
  5. Step 5: Solve for x
    x = 224,130,841/9,738
  6. Step 6: Final answer
    x = 23,016.11

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.