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Finding the Third Proportional to 414.49 and 977.06

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Solution

The third proportional to 414.49 and 977.06 is: 2,303.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    414.49 : 977.06 = 977.06 : x
  2. Step 2: Convert to fraction form
    414.49/977.06 = 977.06/x
  3. Step 3: Cross multiply
    414.49x = 977.06 × 977.06
  4. Step 4: Simplify right side
    414.49x = 954,651.13
  5. Step 5: Solve for x
    x = 954,651.13/414.49
  6. Step 6: Final answer
    x = 2,303.18

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.