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Finding the Third Proportional to 680 and 1,014

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Solution

The third proportional to 680 and 1,014 is: 1,512.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    680 : 1,014 = 1,014 : x
  2. Step 2: Convert to fraction form
    680/1,014 = 1,014/x
  3. Step 3: Cross multiply
    680x = 1,014 × 1,014
  4. Step 4: Simplify right side
    680x = 1,028,196
  5. Step 5: Solve for x
    x = 1,028,196/680
  6. Step 6: Final answer
    x = 1,512.05

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.