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Finding the Fourth Proportional to 1,042.45, 1,564.10 and 457.14

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Solution

The fourth proportional to 1,042.45, 1,564.10 and 457.14 is: 685.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,042.45 : 1,564.10 = 457.14 : x
  2. Step 2: Convert to fraction form
    1,042.45/1,564.10 = 457.14/x
  3. Step 3: Cross multiply
    1,042.45x = 1,564.10 × 457.14
  4. Step 4: Simplify right side
    1,042.45x = 715,020.54
  5. Step 5: Solve for x
    x = 715,020.54/1,042.45
  6. Step 6: Final answer
    x = 685.91

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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.