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Finding the Third Proportional to 1,042 and 1,683

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Solution

The third proportional to 1,042 and 1,683 is: 2,718.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,042 : 1,683 = 1,683 : x
  2. Step 2: Convert to fraction form
    1,042/1,683 = 1,683/x
  3. Step 3: Cross multiply
    1,042x = 1,683 × 1,683
  4. Step 4: Simplify right side
    1,042x = 2,832,489
  5. Step 5: Solve for x
    x = 2,832,489/1,042
  6. Step 6: Final answer
    x = 2,718.32

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Why These Related Problems?

These problems maintain the same ratio (1.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.