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Finding the Third Proportional to 680 and 1,059

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Solution

The third proportional to 680 and 1,059 is: 1,649.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    680 : 1,059 = 1,059 : x
  2. Step 2: Convert to fraction form
    680/1,059 = 1,059/x
  3. Step 3: Cross multiply
    680x = 1,059 × 1,059
  4. Step 4: Simplify right side
    680x = 1,121,481
  5. Step 5: Solve for x
    x = 1,121,481/680
  6. Step 6: Final answer
    x = 1,649.24

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.