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Finding the Third Proportional to 1,097 and 1,596

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Solution

The third proportional to 1,097 and 1,596 is: 2,321.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,097 : 1,596 = 1,596 : x
  2. Step 2: Convert to fraction form
    1,097/1,596 = 1,596/x
  3. Step 3: Cross multiply
    1,097x = 1,596 × 1,596
  4. Step 4: Simplify right side
    1,097x = 2,547,216
  5. Step 5: Solve for x
    x = 2,547,216/1,097
  6. Step 6: Final answer
    x = 2,321.98

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.