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Finding the Third Proportional to 1,730 and 4,202

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Solution

The third proportional to 1,730 and 4,202 is: 10,206.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,730 : 4,202 = 4,202 : x
  2. Step 2: Convert to fraction form
    1,730/4,202 = 4,202/x
  3. Step 3: Cross multiply
    1,730x = 4,202 × 4,202
  4. Step 4: Simplify right side
    1,730x = 17,656,804
  5. Step 5: Solve for x
    x = 17,656,804/1,730
  6. Step 6: Final answer
    x = 10,206.25

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.