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Finding the Fourth Proportional to 1,564.25, 2,346.51 and 410

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Solution

The fourth proportional to 1,564.25, 2,346.51 and 410 is: 615.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,564.25 : 2,346.51 = 410 : x
  2. Step 2: Convert to fraction form
    1,564.25/2,346.51 = 410/x
  3. Step 3: Cross multiply
    1,564.25x = 2,346.51 × 410
  4. Step 4: Simplify right side
    1,564.25x = 962,069.10
  5. Step 5: Solve for x
    x = 962,069.10/1,564.25
  6. Step 6: Final answer
    x = 615.04

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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.