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Finding the Third Proportional to 51,096 and 77,724

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Solution

The third proportional to 51,096 and 77,724 is: 118,228.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,096 : 77,724 = 77,724 : x
  2. Step 2: Convert to fraction form
    51,096/77,724 = 77,724/x
  3. Step 3: Cross multiply
    51,096x = 77,724 × 77,724
  4. Step 4: Simplify right side
    51,096x = 6,041,020,176
  5. Step 5: Solve for x
    x = 6,041,020,176/51,096
  6. Step 6: Final answer
    x = 118,228.83

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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.