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Finding the Third Proportional to 431.75 and 678.25

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Solution

The third proportional to 431.75 and 678.25 is: 1,065.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    431.75 : 678.25 = 678.25 : x
  2. Step 2: Convert to fraction form
    431.75/678.25 = 678.25/x
  3. Step 3: Cross multiply
    431.75x = 678.25 × 678.25
  4. Step 4: Simplify right side
    431.75x = 460,023.06
  5. Step 5: Solve for x
    x = 460,023.06/431.75
  6. Step 6: Final answer
    x = 1,065.48

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.