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Finding the Third Proportional to 1,417 and 2,052

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Solution

The third proportional to 1,417 and 2,052 is: 2,971.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,417 : 2,052 = 2,052 : x
  2. Step 2: Convert to fraction form
    1,417/2,052 = 2,052/x
  3. Step 3: Cross multiply
    1,417x = 2,052 × 2,052
  4. Step 4: Simplify right side
    1,417x = 4,210,704
  5. Step 5: Solve for x
    x = 4,210,704/1,417
  6. Step 6: Final answer
    x = 2,971.56

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.