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Finding the Fourth Proportional to 419.32, 580.14 and 410.08

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Solution

The fourth proportional to 419.32, 580.14 and 410.08 is: 567.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.32 : 580.14 = 410.08 : x
  2. Step 2: Convert to fraction form
    419.32/580.14 = 410.08/x
  3. Step 3: Cross multiply
    419.32x = 580.14 × 410.08
  4. Step 4: Simplify right side
    419.32x = 237,903.81
  5. Step 5: Solve for x
    x = 237,903.81/419.32
  6. Step 6: Final answer
    x = 567.36

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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.