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Finding the Third Proportional to 164 and 259

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Solution

The third proportional to 164 and 259 is: 409.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    164 : 259 = 259 : x
  2. Step 2: Convert to fraction form
    164/259 = 259/x
  3. Step 3: Cross multiply
    164x = 259 × 259
  4. Step 4: Simplify right side
    164x = 67,081
  5. Step 5: Solve for x
    x = 67,081/164
  6. Step 6: Final answer
    x = 409.03

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.