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Finding the Third Proportional to 419.75 and 590

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Solution

The third proportional to 419.75 and 590 is: 829.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    419.75 : 590 = 590 : x
  2. Step 2: Convert to fraction form
    419.75/590 = 590/x
  3. Step 3: Cross multiply
    419.75x = 590 × 590
  4. Step 4: Simplify right side
    419.75x = 348,100
  5. Step 5: Solve for x
    x = 348,100/419.75
  6. Step 6: Final answer
    x = 829.30

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.