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Finding the Third Proportional to 1,585 and 1,853

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Solution

The third proportional to 1,585 and 1,853 is: 2,166.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,585 : 1,853 = 1,853 : x
  2. Step 2: Convert to fraction form
    1,585/1,853 = 1,853/x
  3. Step 3: Cross multiply
    1,585x = 1,853 × 1,853
  4. Step 4: Simplify right side
    1,585x = 3,433,609
  5. Step 5: Solve for x
    x = 3,433,609/1,585
  6. Step 6: Final answer
    x = 2,166.31

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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.