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Finding the Third Proportional to 678 and 772.50

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Solution

The third proportional to 678 and 772.50 is: 880.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 772.50 = 772.50 : x
  2. Step 2: Convert to fraction form
    678/772.50 = 772.50/x
  3. Step 3: Cross multiply
    678x = 772.50 × 772.50
  4. Step 4: Simplify right side
    678x = 596,756.25
  5. Step 5: Solve for x
    x = 596,756.25/678
  6. Step 6: Final answer
    x = 880.17

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.