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Finding the Third Proportional to 1,688 and 1,823

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Solution

The third proportional to 1,688 and 1,823 is: 1,968.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,688 : 1,823 = 1,823 : x
  2. Step 2: Convert to fraction form
    1,688/1,823 = 1,823/x
  3. Step 3: Cross multiply
    1,688x = 1,823 × 1,823
  4. Step 4: Simplify right side
    1,688x = 3,323,329
  5. Step 5: Solve for x
    x = 3,323,329/1,688
  6. Step 6: Final answer
    x = 1,968.80

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.