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Finding the Third Proportional to 208.50 and 314.25

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Solution

The third proportional to 208.50 and 314.25 is: 473.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    208.50 : 314.25 = 314.25 : x
  2. Step 2: Convert to fraction form
    208.50/314.25 = 314.25/x
  3. Step 3: Cross multiply
    208.50x = 314.25 × 314.25
  4. Step 4: Simplify right side
    208.50x = 98,753.06
  5. Step 5: Solve for x
    x = 98,753.06/208.50
  6. Step 6: Final answer
    x = 473.64

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.