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Finding the Third Proportional to 51,946 and 77,980

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Solution

The third proportional to 51,946 and 77,980 is: 117,061.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,946 : 77,980 = 77,980 : x
  2. Step 2: Convert to fraction form
    51,946/77,980 = 77,980/x
  3. Step 3: Cross multiply
    51,946x = 77,980 × 77,980
  4. Step 4: Simplify right side
    51,946x = 6,080,880,400
  5. Step 5: Solve for x
    x = 6,080,880,400/51,946
  6. Step 6: Final answer
    x = 117,061.57

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.