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Finding the Third Proportional to 770.75 and 1,678.38

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Solution

The third proportional to 770.75 and 1,678.38 is: 3,654.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    770.75 : 1,678.38 = 1,678.38 : x
  2. Step 2: Convert to fraction form
    770.75/1,678.38 = 1,678.38/x
  3. Step 3: Cross multiply
    770.75x = 1,678.38 × 1,678.38
  4. Step 4: Simplify right side
    770.75x = 2,816,942.64
  5. Step 5: Solve for x
    x = 2,816,942.64/770.75
  6. Step 6: Final answer
    x = 3,654.81

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.