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Finding the Third Proportional to 78 and 189.25

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Solution

The third proportional to 78 and 189.25 is: 459.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    78 : 189.25 = 189.25 : x
  2. Step 2: Convert to fraction form
    78/189.25 = 189.25/x
  3. Step 3: Cross multiply
    78x = 189.25 × 189.25
  4. Step 4: Simplify right side
    78x = 35,815.56
  5. Step 5: Solve for x
    x = 35,815.56/78
  6. Step 6: Final answer
    x = 459.17

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.