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Finding the Fourth Proportional to 1,407.16, 2,109.88 and 586

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Solution

The fourth proportional to 1,407.16, 2,109.88 and 586 is: 878.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407.16 : 2,109.88 = 586 : x
  2. Step 2: Convert to fraction form
    1,407.16/2,109.88 = 586/x
  3. Step 3: Cross multiply
    1,407.16x = 2,109.88 × 586
  4. Step 4: Simplify right side
    1,407.16x = 1,236,389.68
  5. Step 5: Solve for x
    x = 1,236,389.68/1,407.16
  6. Step 6: Final answer
    x = 878.64

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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.