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Finding the Third Proportional to 324 and 678.38

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Solution

The third proportional to 324 and 678.38 is: 1,420.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    324 : 678.38 = 678.38 : x
  2. Step 2: Convert to fraction form
    324/678.38 = 678.38/x
  3. Step 3: Cross multiply
    324x = 678.38 × 678.38
  4. Step 4: Simplify right side
    324x = 460,192.64
  5. Step 5: Solve for x
    x = 460,192.64/324
  6. Step 6: Final answer
    x = 1,420.35

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.