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Finding the Fourth Proportional to 456.68, 684.54 and 213

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Solution

The fourth proportional to 456.68, 684.54 and 213 is: 319.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.68 : 684.54 = 213 : x
  2. Step 2: Convert to fraction form
    456.68/684.54 = 213/x
  3. Step 3: Cross multiply
    456.68x = 684.54 × 213
  4. Step 4: Simplify right side
    456.68x = 145,807.02
  5. Step 5: Solve for x
    x = 145,807.02/456.68
  6. Step 6: Final answer
    x = 319.28

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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.