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Finding the Third Proportional to 490 and 590

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Solution

The third proportional to 490 and 590 is: 710.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    490 : 590 = 590 : x
  2. Step 2: Convert to fraction form
    490/590 = 590/x
  3. Step 3: Cross multiply
    490x = 590 × 590
  4. Step 4: Simplify right side
    490x = 348,100
  5. Step 5: Solve for x
    x = 348,100/490
  6. Step 6: Final answer
    x = 710.41

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These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.