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Finding the Third Proportional to 214.50 and 470.25

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Solution

The third proportional to 214.50 and 470.25 is: 1,030.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.50 : 470.25 = 470.25 : x
  2. Step 2: Convert to fraction form
    214.50/470.25 = 470.25/x
  3. Step 3: Cross multiply
    214.50x = 470.25 × 470.25
  4. Step 4: Simplify right side
    214.50x = 221,135.06
  5. Step 5: Solve for x
    x = 221,135.06/214.50
  6. Step 6: Final answer
    x = 1,030.93

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.