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Finding the Third Proportional to 76 and 180.25

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Solution

The third proportional to 76 and 180.25 is: 427.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    76 : 180.25 = 180.25 : x
  2. Step 2: Convert to fraction form
    76/180.25 = 180.25/x
  3. Step 3: Cross multiply
    76x = 180.25 × 180.25
  4. Step 4: Simplify right side
    76x = 32,490.06
  5. Step 5: Solve for x
    x = 32,490.06/76
  6. Step 6: Final answer
    x = 427.50

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.