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Finding the Third Proportional to 409.75 and 972.88

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Solution

The third proportional to 409.75 and 972.88 is: 2,309.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.75 : 972.88 = 972.88 : x
  2. Step 2: Convert to fraction form
    409.75/972.88 = 972.88/x
  3. Step 3: Cross multiply
    409.75x = 972.88 × 972.88
  4. Step 4: Simplify right side
    409.75x = 946,485.77
  5. Step 5: Solve for x
    x = 946,485.77/409.75
  6. Step 6: Final answer
    x = 2,309.91

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.