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Finding the Third Proportional to 470 and 1,223

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Solution

The third proportional to 470 and 1,223 is: 3,182.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    470 : 1,223 = 1,223 : x
  2. Step 2: Convert to fraction form
    470/1,223 = 1,223/x
  3. Step 3: Cross multiply
    470x = 1,223 × 1,223
  4. Step 4: Simplify right side
    470x = 1,495,729
  5. Step 5: Solve for x
    x = 1,495,729/470
  6. Step 6: Final answer
    x = 3,182.40

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.