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Finding the Fourth Proportional to 686, 1,029.72 and 470

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Solution

The fourth proportional to 686, 1,029.72 and 470 is: 705.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    686 : 1,029.72 = 470 : x
  2. Step 2: Convert to fraction form
    686/1,029.72 = 470/x
  3. Step 3: Cross multiply
    686x = 1,029.72 × 470
  4. Step 4: Simplify right side
    686x = 483,968.40
  5. Step 5: Solve for x
    x = 483,968.40/686
  6. Step 6: Final answer
    x = 705.49

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.