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Finding the Third Proportional to 259 and 470

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Solution

The third proportional to 259 and 470 is: 852.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    259 : 470 = 470 : x
  2. Step 2: Convert to fraction form
    259/470 = 470/x
  3. Step 3: Cross multiply
    259x = 470 × 470
  4. Step 4: Simplify right side
    259x = 220,900
  5. Step 5: Solve for x
    x = 220,900/259
  6. Step 6: Final answer
    x = 852.90

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These problems maintain the same ratio (1.81) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.