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Mixing Problem: Calculating Water Addition Percentage

Mixing Problem: Calculating Water Addition Percentage
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2015-08-11 16:00
FunctionProbability & StatisticsOptimization
In collections Chemistry2
This example demonstrates how to calculate the concentration percentage after adding water to an original solution. The core mathematical concept is the application of linear functions in concentration problems, using the principle of solute mass conservation to establish equations and solve for the new percentage concentration after dilution. Construction highlights: Use GeoGebra's Textfield for inputting initial concentration and water amount, apply LinearFunction to calculate new concentration, and use Sliders to dynamically show concentration changes with varying water additions. This example is suitable for middle school mathematics courses teaching equations, functions, and practical applications of percentages, as well as demonstrating proportional concepts in probability and statistics.

GeoGebra Commands & Parameters

  1. Ray(A_4, B_4) → l
  2. OrthogonalLine(E_4, e_1) → m
  3. Intersect(l, m) → C_4
  4. Line(A_3, B_3) → f
  5. Line(A_2, C_2) → p
  6. Intersect(c, f) → C_3
  7. Textfield(m_11) → inputBoxm_11
  8. Textfield(m_21) → inputBoxm_21
  9. Textfield(w_11) → inputBoxw_11
  10. Textfield(m_32) → inputBoxm_32
  11. Line(A_1, C_1) → b
  12. Intersect(a, b) → B_1
  13. Segment(E_1, C_1) → b_1
  14. Segment(C_1, F_1) → c_1
  15. Segment(D_1, B_1) → a_1
  16. Segment(B_1, G_1) → d_1
  17. Segment(A_1, C_1) → g_1
  18. OrthogonalLine(G_2, t) → q
  19. Intersect(q, p) → B_2
  20. Segment(A_2, C_2) → g_2
  21. Segment(G_2, B_2) → d_2
  22. Segment(B_2, D_2) → a_2
  23. Segment(C_2, E_2) → b_2
  24. Segment(C_2, F_2) → c_2
  25. Segment(G_3, B_3) → d_3
  26. Segment(D_3, B_3) → a_3
  27. Line(B_4, C_4) → i
  28. Segment(G_4, B_4) → d_4
  29. Segment(B_4, D_4) → a_4
  30. Segment(F_4, C_4) → c_4
  31. Segment(C_4, E_4) → b_4
  32. Segment(A_4, C_4) → g_4
  33. Midpoint(D_2, E_2) → S_2
  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_34) → inputBoxm_34
  42. Midpoint(D_1, E_1) → S_1
  43. VerticalText(Oy) → Oyv
  44. VerticalText(text2) → text3
  45. Min(w_13, w_23) → min3
  46. Max(w_13, w_23) → max3
  47. Sequence((100 * n), n, 0, 200) → list1
  48. KeepIf(0 < x ≤ 100, list21) → list31
  49. Element(list31, 1) → elem1
  50. IndexOf(elem1, list21) → index1
  51. Element(list1, index1) → scale
  52. Polygon(H_1, I_1, M_1, L_1) → poly1z1, a_5, b_5, c_5, d_5
  53. Polygon(H_1, I_1, J_1, K_1) → poly1b1, d, e, j, k
  54. Midpoint(D_3, E_3) → S_3
  55. Ray(F_3, C_3) → h
  56. Segment(A_3, C_3) → g_3
  57. Polygon(N_1, O_1, T_1, R_1) → poly1z2, n_1, o_1, t_5, r_5
  58. Polygon(N_1, O_1, P_1, Q_1) → poly1b2, n_2, o_2, p_5, q_5
  59. Polygon(U_1, V_1, W_1, X_1) → poly1b3, u_5, v_1, w_1, x_1
  60. Polygon(U_1, V_1, Z_1, Y_1) → poly1z3, u_6, v_2, z_1, y_1
  61. Segment(F_3, C_3) → c_3
  62. Segment(C_3, E_3) → b_3
  63. Polygon(H_2, I_2, J_2, K_2) → poly2b1, h_2, i_2, j_2, k_5
  64. Polygon(N_2, O_2, P_2, Q_2) → poly2b2, n_3, o_3, p_6, q_6
  65. Polygon(U_2, V_2, W_2, X_2) → poly2b3, u_7, v_3, w_2, x_2
  66. Polygon(H_2, I_2, M_2, L_2) → poly2z1, h_1, i_1, m_2, l_2
  67. Polygon(N_2, O_2, T_2, R_2) → poly2z2, n_4, o_4, t_6, r_6
  68. Polygon(U_2, V_2, Z_2, Y_2) → poly2z3, u_8, v_4, z_2, y_2
  69. Polygon(H_3, I_3, J_3, K_3) → poly3b1, h_3, i_3, j_3, k_6
  70. Polygon(N_3, O_3, P_3, Q_3) → poly3b2, n_5, o_5, p_7, q_7
  71. Polygon(U_3, V_3, W_3, X_3) → poly3b3, u_9, v_5, w_3, x_3
  72. Polygon(H_3, I_3, M_3, L_3) → poly3z1, h_4, i_4, m_1, l_3
  73. Polygon(N_3, O_3, T_3, R_3) → poly3z2, n_6, o_6, t_7, r_7
  74. Polygon(Y_3, U_3, V_3, Z_3) → poly3z3, y_3, u_{10}, v_6, z_3
  75. Polygon(H_4, I_4, J_4, K_4) → poly4b1, h_5, i_5, j_4, k_7
  76. Polygon(N_4, O_4, P_4, Q_4) → poly4b2, n_7, o_7, p_8, q_8
  77. Polygon(U_4, V_4, W_4, X_4) → poly4b3, u_{11}, v_7, w_4, x_4
  78. Polygon(H_4, I_4, M_4, L_4) → poly4z1, h_6, i_6, m_4, l_4
  79. Polygon(N_4, O_4, T_4, R_4) → poly4z2, n_8, o_8, t_8, r_8
  80. Polygon(U_4, V_4, Z_4, Y_4) → poly4z3, u_{12}, v_8, z_4, y_4
  81. Textfield(m_24) → inputBoxm_24
  82. Ray(E_4, C_4) → n
  83. OrthogonalLine(F_2, t) → g

AI Drawing Prompt Reference

Draw a diagram to illustrate how to calculate the concentration percentage after adding water to an original solution. Include a line and a perpendicular line intersecting at point C. Another line intersects the first line at C. Use text fields for inputting initial concentration and water amount, and apply a linear function to calculate the new concentration. Use sliders to dynamically show concentration changes with varying water additions. The diagram also features multiple line segments and several midpoints to represent the geometric changes in concentration.
The prompt above was compiled from the original drawing commands and is for reference only.