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Finding the Third Proportional to 1,410 and 2,942

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Solution

The third proportional to 1,410 and 2,942 is: 6,138.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,410 : 2,942 = 2,942 : x
  2. Step 2: Convert to fraction form
    1,410/2,942 = 2,942/x
  3. Step 3: Cross multiply
    1,410x = 2,942 × 2,942
  4. Step 4: Simplify right side
    1,410x = 8,655,364
  5. Step 5: Solve for x
    x = 8,655,364/1,410
  6. Step 6: Final answer
    x = 6,138.56

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.