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Finding the Third Proportional to 259.75 and 410.38

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Solution

The third proportional to 259.75 and 410.38 is: 648.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    259.75 : 410.38 = 410.38 : x
  2. Step 2: Convert to fraction form
    259.75/410.38 = 410.38/x
  3. Step 3: Cross multiply
    259.75x = 410.38 × 410.38
  4. Step 4: Simplify right side
    259.75x = 168,407.64
  5. Step 5: Solve for x
    x = 168,407.64/259.75
  6. Step 6: Final answer
    x = 648.35

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.