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Finding the Third Proportional to 456 and 691.50

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Solution

The third proportional to 456 and 691.50 is: 1,048.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    456 : 691.50 = 691.50 : x
  2. Step 2: Convert to fraction form
    456/691.50 = 691.50/x
  3. Step 3: Cross multiply
    456x = 691.50 × 691.50
  4. Step 4: Simplify right side
    456x = 478,172.25
  5. Step 5: Solve for x
    x = 478,172.25/456
  6. Step 6: Final answer
    x = 1,048.62

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.