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Finding the Third Proportional to 2,306 and 2,946

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Solution

The third proportional to 2,306 and 2,946 is: 3,763.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,306 : 2,946 = 2,946 : x
  2. Step 2: Convert to fraction form
    2,306/2,946 = 2,946/x
  3. Step 3: Cross multiply
    2,306x = 2,946 × 2,946
  4. Step 4: Simplify right side
    2,306x = 8,678,916
  5. Step 5: Solve for x
    x = 8,678,916/2,306
  6. Step 6: Final answer
    x = 3,763.62

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.