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Finding the Third Proportional to 6,840 and 9,724

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Solution

The third proportional to 6,840 and 9,724 is: 13,824.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,840 : 9,724 = 9,724 : x
  2. Step 2: Convert to fraction form
    6,840/9,724 = 9,724/x
  3. Step 3: Cross multiply
    6,840x = 9,724 × 9,724
  4. Step 4: Simplify right side
    6,840x = 94,556,176
  5. Step 5: Solve for x
    x = 94,556,176/6,840
  6. Step 6: Final answer
    x = 13,824.00

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.