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Finding the Third Proportional to 1,014 and 1,416.75

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Solution

The third proportional to 1,014 and 1,416.75 is: 1,979.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,014 : 1,416.75 = 1,416.75 : x
  2. Step 2: Convert to fraction form
    1,014/1,416.75 = 1,416.75/x
  3. Step 3: Cross multiply
    1,014x = 1,416.75 × 1,416.75
  4. Step 4: Simplify right side
    1,014x = 2,007,180.56
  5. Step 5: Solve for x
    x = 2,007,180.56/1,014
  6. Step 6: Final answer
    x = 1,979.47

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.