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Finding the Third Proportional to 1,410 and 2,071

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Solution

The third proportional to 1,410 and 2,071 is: 3,041.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,410 : 2,071 = 2,071 : x
  2. Step 2: Convert to fraction form
    1,410/2,071 = 2,071/x
  3. Step 3: Cross multiply
    1,410x = 2,071 × 2,071
  4. Step 4: Simplify right side
    1,410x = 4,289,041
  5. Step 5: Solve for x
    x = 4,289,041/1,410
  6. Step 6: Final answer
    x = 3,041.87

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.