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Finding the Third Proportional to 1,306 and 2,854

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Solution

The third proportional to 1,306 and 2,854 is: 6,236.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,306 : 2,854 = 2,854 : x
  2. Step 2: Convert to fraction form
    1,306/2,854 = 2,854/x
  3. Step 3: Cross multiply
    1,306x = 2,854 × 2,854
  4. Step 4: Simplify right side
    1,306x = 8,145,316
  5. Step 5: Solve for x
    x = 8,145,316/1,306
  6. Step 6: Final answer
    x = 6,236.84

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.