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Finding the Third Proportional to 429 and 1,010

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Solution

The third proportional to 429 and 1,010 is: 2,377.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    429 : 1,010 = 1,010 : x
  2. Step 2: Convert to fraction form
    429/1,010 = 1,010/x
  3. Step 3: Cross multiply
    429x = 1,010 × 1,010
  4. Step 4: Simplify right side
    429x = 1,020,100
  5. Step 5: Solve for x
    x = 1,020,100/429
  6. Step 6: Final answer
    x = 2,377.86

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.