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Finding the Fourth Proportional to 865, 1,297.50 and 257

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Solution

The fourth proportional to 865, 1,297.50 and 257 is: 385.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    865 : 1,297.50 = 257 : x
  2. Step 2: Convert to fraction form
    865/1,297.50 = 257/x
  3. Step 3: Cross multiply
    865x = 1,297.50 × 257
  4. Step 4: Simplify right side
    865x = 333,457.50
  5. Step 5: Solve for x
    x = 333,457.50/865
  6. Step 6: Final answer
    x = 385.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.