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Finding the Third Proportional to 51,416 and 77,772

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Solution

The third proportional to 51,416 and 77,772 is: 117,638.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,416 : 77,772 = 77,772 : x
  2. Step 2: Convert to fraction form
    51,416/77,772 = 77,772/x
  3. Step 3: Cross multiply
    51,416x = 77,772 × 77,772
  4. Step 4: Simplify right side
    51,416x = 6,048,483,984
  5. Step 5: Solve for x
    x = 6,048,483,984/51,416
  6. Step 6: Final answer
    x = 117,638.17

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.