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Finding the Fourth Proportional to 1,109.71, 1,664.57 and 460.43

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Solution

The fourth proportional to 1,109.71, 1,664.57 and 460.43 is: 690.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,109.71 : 1,664.57 = 460.43 : x
  2. Step 2: Convert to fraction form
    1,109.71/1,664.57 = 460.43/x
  3. Step 3: Cross multiply
    1,109.71x = 1,664.57 × 460.43
  4. Step 4: Simplify right side
    1,109.71x = 766,417.97
  5. Step 5: Solve for x
    x = 766,417.97/1,109.71
  6. Step 6: Final answer
    x = 690.65

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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.