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Finding the Fourth Proportional to 1,023.14, 1,412.15 and 709.07

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Solution

The fourth proportional to 1,023.14, 1,412.15 and 709.07 is: 978.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023.14 : 1,412.15 = 709.07 : x
  2. Step 2: Convert to fraction form
    1,023.14/1,412.15 = 709.07/x
  3. Step 3: Cross multiply
    1,023.14x = 1,412.15 × 709.07
  4. Step 4: Simplify right side
    1,023.14x = 1,001,302.59
  5. Step 5: Solve for x
    x = 1,001,302.59/1,023.14
  6. Step 6: Final answer
    x = 978.66

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.