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Finding the Third Proportional to 120 and 256.50

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Solution

The third proportional to 120 and 256.50 is: 548.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    120 : 256.50 = 256.50 : x
  2. Step 2: Convert to fraction form
    120/256.50 = 256.50/x
  3. Step 3: Cross multiply
    120x = 256.50 × 256.50
  4. Step 4: Simplify right side
    120x = 65,792.25
  5. Step 5: Solve for x
    x = 65,792.25/120
  6. Step 6: Final answer
    x = 548.27

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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.