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Finding the Third Proportional to 1,296 and 2,053

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Solution

The third proportional to 1,296 and 2,053 is: 3,252.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,296 : 2,053 = 2,053 : x
  2. Step 2: Convert to fraction form
    1,296/2,053 = 2,053/x
  3. Step 3: Cross multiply
    1,296x = 2,053 × 2,053
  4. Step 4: Simplify right side
    1,296x = 4,214,809
  5. Step 5: Solve for x
    x = 4,214,809/1,296
  6. Step 6: Final answer
    x = 3,252.17

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.