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Finding the Third Proportional to 456.19 and 856.69

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Solution

The third proportional to 456.19 and 856.69 is: 1,608.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.19 : 856.69 = 856.69 : x
  2. Step 2: Convert to fraction form
    456.19/856.69 = 856.69/x
  3. Step 3: Cross multiply
    456.19x = 856.69 × 856.69
  4. Step 4: Simplify right side
    456.19x = 733,913.47
  5. Step 5: Solve for x
    x = 733,913.47/456.19
  6. Step 6: Final answer
    x = 1,608.80

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.