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Finding the Fourth Proportional to 1,315.78, 1,976.29 and 823.06

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Solution

The fourth proportional to 1,315.78, 1,976.29 and 823.06 is: 1,236.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,315.78 : 1,976.29 = 823.06 : x
  2. Step 2: Convert to fraction form
    1,315.78/1,976.29 = 823.06/x
  3. Step 3: Cross multiply
    1,315.78x = 1,976.29 × 823.06
  4. Step 4: Simplify right side
    1,315.78x = 1,626,608.75
  5. Step 5: Solve for x
    x = 1,626,608.75/1,315.78
  6. Step 6: Final answer
    x = 1,236.23

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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.