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Finding the Fourth Proportional to 1,564.03, 2,346.05 and 409.78

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Solution

The fourth proportional to 1,564.03, 2,346.05 and 409.78 is: 614.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,564.03 : 2,346.05 = 409.78 : x
  2. Step 2: Convert to fraction form
    1,564.03/2,346.05 = 409.78/x
  3. Step 3: Cross multiply
    1,564.03x = 2,346.05 × 409.78
  4. Step 4: Simplify right side
    1,564.03x = 961,364.37
  5. Step 5: Solve for x
    x = 961,364.37/1,564.03
  6. Step 6: Final answer
    x = 614.67

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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.