silemus.
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  1. 4No solution, linear system
  2. 5Infinite solutions, linear system
  3. 15Probability from a table
  4. 18Median from a frequency table
  5. 22One solution, discriminant=0
  6. 23Max height of a parabola
  7. 25Exponential decay, 15% off
  8. 29Composing f and g
  9. 32Radius from two points
  10. 33Arc length from central angle
  11. 37Similar triangles ratio
  12. 47Two-ticket system of equations
  13. 51No solution, linear equation
  14. 52Taxi cost inequality
  15. 55Scaling 9x-6y+5
  16. 56Costly text message inequality
  17. 59Solving a square root equation
  18. 62Factor theorem on a cubic
  19. 64Percent growth per year
  20. 66x²+y² from sum and product
  21. 67Sum of roots of intersection
  22. 70Completing the square
  23. 73Percent off, then tax
  24. 74Mean with a score removed
  25. 75Overlapping sets, neither
  26. 81Percent of a percent
  27. 82Average speed, unequal times
  28. 85Fraction of a subgroup
  29. 86Mixing to a target percent
  30. 92Inscribed angle theorem
  31. 93Circle from diameter endpoints
  32. 96Sine-cosine complementary angles
  33. 97Area ratio of similar triangles
  34. 98Diagonal of a rectangle
  35. 100Right triangle, tan from cos
  36. 101Volume displaced raises water

47Two-ticket system of equations

A theater sold 250 tickets for a show. Adult tickets cost 12 dollars each and student tickets cost 8 dollars each. The theater collected 2,600 dollars in total. How many adult tickets were sold? A) 100 B) 125 C) 150 D) 200

150 adult tickets were sold, matching choice C. Setting a + s = 250 and 12a + 8s = 2600, substituting s = 250 − a gives 4a = 600, so a = 150. Check: 12(150) + 8(100) = 2600.

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