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Finding the Third Proportional to 1,596 and 2,154

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Solution

The third proportional to 1,596 and 2,154 is: 2,907.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,596 : 2,154 = 2,154 : x
  2. Step 2: Convert to fraction form
    1,596/2,154 = 2,154/x
  3. Step 3: Cross multiply
    1,596x = 2,154 × 2,154
  4. Step 4: Simplify right side
    1,596x = 4,639,716
  5. Step 5: Solve for x
    x = 4,639,716/1,596
  6. Step 6: Final answer
    x = 2,907.09

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.