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Mixture Problems - Adding Water Graphical Solution

Mixture Problems - Adding Water Graphical Solution
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2015-03-12 19:14
Coordinate GeometryGeometric ConstructionGraphing
This example demonstrates the graphical solution of mixture problems involving the addition of water, visualizing concentration changes. Core math concepts include ratios, concentration calculations, linear equations, and graphical representation. GeoGebra commands and objects used in construction are highlighted from the summary, such as Line, Intersect, Segment, OrthogonalLine, and Midpoint. Suitable for middle school and above students to understand the integration of graphical methods with mixture problem solving.

GeoGebra Commands & Parameters

  1. Line(B_4, A_4) → i
  2. Intersect(i, d) → C_4
  3. Textfield(m_11) → inputBoxm_11
  4. Textfield(m_21) → inputBoxm_21
  5. Textfield(w_11) → inputBoxw_11
  6. Textfield(m_32) → inputBoxm_32
  7. Line(A_1, C_1) → b
  8. Intersect(a, b) → B_1
  9. Segment(E_1, C_1) → b_1
  10. Segment(C_1, F_1) → c_1
  11. Segment(D_1, B_1) → a_1
  12. Segment(B_1, G_1) → d_1
  13. Segment(A_1, C_1) → g_1
  14. Line(A_2, C_2) → p
  15. OrthogonalLine(G_2, yAxis) → q
  16. Intersect(q, p) → B_2
  17. Segment(A_2, C_2) → g_2
  18. Segment(G_2, B_2) → d_2
  19. Segment(B_2, D_2) → a_2
  20. Segment(C_2, E_2) → b_2
  21. Line(A_3, B_3) → c
  22. Segment(C_2, F_2) → c_2
  23. Line(A_3, B_3) → f
  24. OrthogonalLine(F_3, yAxis) → g
  25. Intersect(g, f) → C_3
  26. Segment(G_3, B_3) → d_3
  27. Segment(D_3, B_3) → a_3
  28. Segment(E_3, C_3) → b_3
  29. Segment(C_3, F_3) → c_3
  30. Segment(G_4, B_4) → d_4
  31. Segment(B_4, D_4) → a_4
  32. Midpoint(D_2, E_2) → S_2
  33. Midpoint(D_3, E_3) → S_3
  34. Midpoint(D_4, E_4) → S_4
  35. Textfield(w_12) → inputBoxw_12
  36. Textfield(w_13) → inputBoxw_13
  37. Textfield(w_33) → inputBoxw_33
  38. Textfield(m_13) → inputBoxm_13
  39. Textfield(w_32) → inputBoxw_32
  40. Textfield(w_34) → inputBoxw_34
  41. Textfield(m_24) → inputBoxm_14
  42. Textfield(m_34) → inputBoxm_34
  43. Midpoint(D_1, E_1) → S_1
  44. Segment(F_4, C_4) → c_4
  45. Segment(E_4, C_4) → b_4
  46. VerticalText(Oy) → Oyv
  47. VerticalText(Oy2) → Oy2v
  48. Polygon(A, B, C, D) → poly1, a_5, b_5, c_5, d_5
  49. Vector(A, D) → u
  50. Translate(A, u) → A'
  51. Translate(B, u) → B'
  52. Translate(C, u) → C'
  53. Translate(D, u) → D'
  54. Polygon(A', B', C', D') → poly1', a', b', c', d'
  55. Translate(A, Vector[(2 * u)]) → A'_1
  56. Translate(B, Vector[(2 * u)]) → B'_1
  57. Translate(C, Vector[(2 * u)]) → C'_1
  58. Translate(D, Vector[(2 * u)]) → D'_1
  59. Polygon(A'_1, B'_1, C'_1, D'_1) → poly1'_1, a'_1, b'_1, c'_1, d'_1
  60. Point(a_5) → E
  61. Point(c'_1) → F
  62. Segment(E, F) → e
  63. Segment(A_3, C_3) → g_3
  64. Ray(F_3, C_3) → h
  65. Segment(A_4, C_4) → g_4
  66. Ray(E_4, C_4) → j