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Finding the Third Proportional to 288.75 and 409.13

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Solution

The third proportional to 288.75 and 409.13 is: 579.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    288.75 : 409.13 = 409.13 : x
  2. Step 2: Convert to fraction form
    288.75/409.13 = 409.13/x
  3. Step 3: Cross multiply
    288.75x = 409.13 × 409.13
  4. Step 4: Simplify right side
    288.75x = 167,383.27
  5. Step 5: Solve for x
    x = 167,383.27/288.75
  6. Step 6: Final answer
    x = 579.68

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.