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Finding the Third Proportional to 1,830 and 2,046

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Solution

The third proportional to 1,830 and 2,046 is: 2,287.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,830 : 2,046 = 2,046 : x
  2. Step 2: Convert to fraction form
    1,830/2,046 = 2,046/x
  3. Step 3: Cross multiply
    1,830x = 2,046 × 2,046
  4. Step 4: Simplify right side
    1,830x = 4,186,116
  5. Step 5: Solve for x
    x = 4,186,116/1,830
  6. Step 6: Final answer
    x = 2,287.50

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Why These Related Problems?

These problems maintain the same ratio (1.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.