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Finding the Third Proportional to 1,570 and 2,099

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Solution

The third proportional to 1,570 and 2,099 is: 2,806.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,570 : 2,099 = 2,099 : x
  2. Step 2: Convert to fraction form
    1,570/2,099 = 2,099/x
  3. Step 3: Cross multiply
    1,570x = 2,099 × 2,099
  4. Step 4: Simplify right side
    1,570x = 4,405,801
  5. Step 5: Solve for x
    x = 4,405,801/1,570
  6. Step 6: Final answer
    x = 2,806.24

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.