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Finding the Third Proportional to 19,970 and 31,312

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Solution

The third proportional to 19,970 and 31,312 is: 49,095.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,970 : 31,312 = 31,312 : x
  2. Step 2: Convert to fraction form
    19,970/31,312 = 31,312/x
  3. Step 3: Cross multiply
    19,970x = 31,312 × 31,312
  4. Step 4: Simplify right side
    19,970x = 980,441,344
  5. Step 5: Solve for x
    x = 980,441,344/19,970
  6. Step 6: Final answer
    x = 49,095.71

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.