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Finding the Third Proportional to 705.75 and 856.50

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Solution

The third proportional to 705.75 and 856.50 is: 1,039.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    705.75 : 856.50 = 856.50 : x
  2. Step 2: Convert to fraction form
    705.75/856.50 = 856.50/x
  3. Step 3: Cross multiply
    705.75x = 856.50 × 856.50
  4. Step 4: Simplify right side
    705.75x = 733,592.25
  5. Step 5: Solve for x
    x = 733,592.25/705.75
  6. Step 6: Final answer
    x = 1,039.45

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.