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Finding the Fourth Proportional to 1,384, 2,075.32 and 410

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Solution

The fourth proportional to 1,384, 2,075.32 and 410 is: 614.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,384 : 2,075.32 = 410 : x
  2. Step 2: Convert to fraction form
    1,384/2,075.32 = 410/x
  3. Step 3: Cross multiply
    1,384x = 2,075.32 × 410
  4. Step 4: Simplify right side
    1,384x = 850,881.20
  5. Step 5: Solve for x
    x = 850,881.20/1,384
  6. Step 6: Final answer
    x = 614.80

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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.