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Finding the Third Proportional to 1,409 and 1,622

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Solution

The third proportional to 1,409 and 1,622 is: 1,867.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,409 : 1,622 = 1,622 : x
  2. Step 2: Convert to fraction form
    1,409/1,622 = 1,622/x
  3. Step 3: Cross multiply
    1,409x = 1,622 × 1,622
  4. Step 4: Simplify right side
    1,409x = 2,630,884
  5. Step 5: Solve for x
    x = 2,630,884/1,409
  6. Step 6: Final answer
    x = 1,867.20

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.