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Finding the Third Proportional to 51,164 and 77,541

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Solution

The third proportional to 51,164 and 77,541 is: 117,516.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,164 : 77,541 = 77,541 : x
  2. Step 2: Convert to fraction form
    51,164/77,541 = 77,541/x
  3. Step 3: Cross multiply
    51,164x = 77,541 × 77,541
  4. Step 4: Simplify right side
    51,164x = 6,012,606,681
  5. Step 5: Solve for x
    x = 6,012,606,681/51,164
  6. Step 6: Final answer
    x = 117,516.35

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.