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Finding the Third Proportional to 729 and 1,290

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Solution

The third proportional to 729 and 1,290 is: 2,282.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    729 : 1,290 = 1,290 : x
  2. Step 2: Convert to fraction form
    729/1,290 = 1,290/x
  3. Step 3: Cross multiply
    729x = 1,290 × 1,290
  4. Step 4: Simplify right side
    729x = 1,664,100
  5. Step 5: Solve for x
    x = 1,664,100/729
  6. Step 6: Final answer
    x = 2,282.72

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.