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Finding the Third Proportional to 31,824 and 69,312

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Solution

The third proportional to 31,824 and 69,312 is: 150,960.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,824 : 69,312 = 69,312 : x
  2. Step 2: Convert to fraction form
    31,824/69,312 = 69,312/x
  3. Step 3: Cross multiply
    31,824x = 69,312 × 69,312
  4. Step 4: Simplify right side
    31,824x = 4,804,153,344
  5. Step 5: Solve for x
    x = 4,804,153,344/31,824
  6. Step 6: Final answer
    x = 150,960.07

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.