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Finding the Third Proportional to 416 and 678.50

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Solution

The third proportional to 416 and 678.50 is: 1,106.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 678.50 = 678.50 : x
  2. Step 2: Convert to fraction form
    416/678.50 = 678.50/x
  3. Step 3: Cross multiply
    416x = 678.50 × 678.50
  4. Step 4: Simplify right side
    416x = 460,362.25
  5. Step 5: Solve for x
    x = 460,362.25/416
  6. Step 6: Final answer
    x = 1,106.64

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.