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Finding the Third Proportional to 853 and 1,296.50

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Solution

The third proportional to 853 and 1,296.50 is: 1,970.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    853 : 1,296.50 = 1,296.50 : x
  2. Step 2: Convert to fraction form
    853/1,296.50 = 1,296.50/x
  3. Step 3: Cross multiply
    853x = 1,296.50 × 1,296.50
  4. Step 4: Simplify right side
    853x = 1,680,912.25
  5. Step 5: Solve for x
    x = 1,680,912.25/853
  6. Step 6: Final answer
    x = 1,970.59

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.