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Finding the Third Proportional to 120,200 and 257,078

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Solution

The third proportional to 120,200 and 257,078 is: 549,826.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,200 : 257,078 = 257,078 : x
  2. Step 2: Convert to fraction form
    120,200/257,078 = 257,078/x
  3. Step 3: Cross multiply
    120,200x = 257,078 × 257,078
  4. Step 4: Simplify right side
    120,200x = 66,089,098,084
  5. Step 5: Solve for x
    x = 66,089,098,084/120,200
  6. Step 6: Final answer
    x = 549,826.11

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.