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Finding the Third Proportional to 678.94 and 828.56

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Solution

The third proportional to 678.94 and 828.56 is: 1,011.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    678.94 : 828.56 = 828.56 : x
  2. Step 2: Convert to fraction form
    678.94/828.56 = 828.56/x
  3. Step 3: Cross multiply
    678.94x = 828.56 × 828.56
  4. Step 4: Simplify right side
    678.94x = 686,515.82
  5. Step 5: Solve for x
    x = 686,515.82/678.94
  6. Step 6: Final answer
    x = 1,011.16

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.