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Finding the Third Proportional to 416 and 681.50

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Solution

The third proportional to 416 and 681.50 is: 1,116.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 681.50 = 681.50 : x
  2. Step 2: Convert to fraction form
    416/681.50 = 681.50/x
  3. Step 3: Cross multiply
    416x = 681.50 × 681.50
  4. Step 4: Simplify right side
    416x = 464,442.25
  5. Step 5: Solve for x
    x = 464,442.25/416
  6. Step 6: Final answer
    x = 1,116.45

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.