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Finding the Third Proportional to 458.26 and 709.07

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Solution

The third proportional to 458.26 and 709.07 is: 1,097.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    458.26 : 709.07 = 709.07 : x
  2. Step 2: Convert to fraction form
    458.26/709.07 = 709.07/x
  3. Step 3: Cross multiply
    458.26x = 709.07 × 709.07
  4. Step 4: Simplify right side
    458.26x = 502,775.17
  5. Step 5: Solve for x
    x = 502,775.17/458.26
  6. Step 6: Final answer
    x = 1,097.14

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.