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Finding the Third Proportional to 1,678 and 1,984

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Solution

The third proportional to 1,678 and 1,984 is: 2,345.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,678 : 1,984 = 1,984 : x
  2. Step 2: Convert to fraction form
    1,678/1,984 = 1,984/x
  3. Step 3: Cross multiply
    1,678x = 1,984 × 1,984
  4. Step 4: Simplify right side
    1,678x = 3,936,256
  5. Step 5: Solve for x
    x = 3,936,256/1,678
  6. Step 6: Final answer
    x = 2,345.80

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.