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Finding the Third Proportional to 415.75 and 689.25

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Solution

The third proportional to 415.75 and 689.25 is: 1,142.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.75 : 689.25 = 689.25 : x
  2. Step 2: Convert to fraction form
    415.75/689.25 = 689.25/x
  3. Step 3: Cross multiply
    415.75x = 689.25 × 689.25
  4. Step 4: Simplify right side
    415.75x = 475,065.56
  5. Step 5: Solve for x
    x = 475,065.56/415.75
  6. Step 6: Final answer
    x = 1,142.67

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.