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Finding the Third Proportional to 416 and 978

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Solution

The third proportional to 416 and 978 is: 2,299.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 978 = 978 : x
  2. Step 2: Convert to fraction form
    416/978 = 978/x
  3. Step 3: Cross multiply
    416x = 978 × 978
  4. Step 4: Simplify right side
    416x = 956,484
  5. Step 5: Solve for x
    x = 956,484/416
  6. Step 6: Final answer
    x = 2,299.24

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These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.