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Finding the Third Proportional to 164 and 284

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Solution

The third proportional to 164 and 284 is: 491.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    164 : 284 = 284 : x
  2. Step 2: Convert to fraction form
    164/284 = 284/x
  3. Step 3: Cross multiply
    164x = 284 × 284
  4. Step 4: Simplify right side
    164x = 80,656
  5. Step 5: Solve for x
    x = 80,656/164
  6. Step 6: Final answer
    x = 491.80

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Why These Related Problems?

These problems maintain the same ratio (1.73) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.