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Finding the Third Proportional to 421.50 and 589.13

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Solution

The third proportional to 421.50 and 589.13 is: 823.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    421.50 : 589.13 = 589.13 : x
  2. Step 2: Convert to fraction form
    421.50/589.13 = 589.13/x
  3. Step 3: Cross multiply
    421.50x = 589.13 × 589.13
  4. Step 4: Simplify right side
    421.50x = 347,068.27
  5. Step 5: Solve for x
    x = 347,068.27/421.50
  6. Step 6: Final answer
    x = 823.41

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.