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Finding the Third Proportional to 782.50 and 1,210

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Solution

The third proportional to 782.50 and 1,210 is: 1,871.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    782.50 : 1,210 = 1,210 : x
  2. Step 2: Convert to fraction form
    782.50/1,210 = 1,210/x
  3. Step 3: Cross multiply
    782.50x = 1,210 × 1,210
  4. Step 4: Simplify right side
    782.50x = 1,464,100
  5. Step 5: Solve for x
    x = 1,464,100/782.50
  6. Step 6: Final answer
    x = 1,871.05

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.