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Finding the Third Proportional to 7,500 and 9,742.50

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Solution

The third proportional to 7,500 and 9,742.50 is: 12,655.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,500 : 9,742.50 = 9,742.50 : x
  2. Step 2: Convert to fraction form
    7,500/9,742.50 = 9,742.50/x
  3. Step 3: Cross multiply
    7,500x = 9,742.50 × 9,742.50
  4. Step 4: Simplify right side
    7,500x = 94,916,306.25
  5. Step 5: Solve for x
    x = 94,916,306.25/7,500
  6. Step 6: Final answer
    x = 12,655.51

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.