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Finding the Third Proportional to 765.75 and 1,213.50

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Solution

The third proportional to 765.75 and 1,213.50 is: 1,923.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    765.75 : 1,213.50 = 1,213.50 : x
  2. Step 2: Convert to fraction form
    765.75/1,213.50 = 1,213.50/x
  3. Step 3: Cross multiply
    765.75x = 1,213.50 × 1,213.50
  4. Step 4: Simplify right side
    765.75x = 1,472,582.25
  5. Step 5: Solve for x
    x = 1,472,582.25/765.75
  6. Step 6: Final answer
    x = 1,923.06

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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.