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Finding the Third Proportional to 1,202 and 1,405

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Solution

The third proportional to 1,202 and 1,405 is: 1,642.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,202 : 1,405 = 1,405 : x
  2. Step 2: Convert to fraction form
    1,202/1,405 = 1,405/x
  3. Step 3: Cross multiply
    1,202x = 1,405 × 1,405
  4. Step 4: Simplify right side
    1,202x = 1,974,025
  5. Step 5: Solve for x
    x = 1,974,025/1,202
  6. Step 6: Final answer
    x = 1,642.28

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.