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Finding the Third Proportional to 410.06 and 538.21

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Solution

The third proportional to 410.06 and 538.21 is: 706.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    410.06 : 538.21 = 538.21 : x
  2. Step 2: Convert to fraction form
    410.06/538.21 = 538.21/x
  3. Step 3: Cross multiply
    410.06x = 538.21 × 538.21
  4. Step 4: Simplify right side
    410.06x = 289,666.81
  5. Step 5: Solve for x
    x = 289,666.81/410.06
  6. Step 6: Final answer
    x = 706.40

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.