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Finding the Third Proportional to 164 and 219

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Solution

The third proportional to 164 and 219 is: 292.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    164 : 219 = 219 : x
  2. Step 2: Convert to fraction form
    164/219 = 219/x
  3. Step 3: Cross multiply
    164x = 219 × 219
  4. Step 4: Simplify right side
    164x = 47,961
  5. Step 5: Solve for x
    x = 47,961/164
  6. Step 6: Final answer
    x = 292.45

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.