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Finding the Third Proportional to 7,278 and 9,827

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Solution

The third proportional to 7,278 and 9,827 is: 13,268.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,278 : 9,827 = 9,827 : x
  2. Step 2: Convert to fraction form
    7,278/9,827 = 9,827/x
  3. Step 3: Cross multiply
    7,278x = 9,827 × 9,827
  4. Step 4: Simplify right side
    7,278x = 96,569,929
  5. Step 5: Solve for x
    x = 96,569,929/7,278
  6. Step 6: Final answer
    x = 13,268.75

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.