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Finding the Third Proportional to 380,078 and 513,043

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Solution

The third proportional to 380,078 and 513,043 is: 692,523.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    380,078 : 513,043 = 513,043 : x
  2. Step 2: Convert to fraction form
    380,078/513,043 = 513,043/x
  3. Step 3: Cross multiply
    380,078x = 513,043 × 513,043
  4. Step 4: Simplify right side
    380,078x = 263,213,119,849
  5. Step 5: Solve for x
    x = 263,213,119,849/380,078
  6. Step 6: Final answer
    x = 692,523.96

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.