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Mixture Problems with Ratios

Mixture Problems with Ratios
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2011-11-19 01:20
Geometric Construction
In collections Unit 1: Ratios and Proportional Relationships
This example demonstrates how to use ratios to model mixture problems using GeoGebra, visually showing the proportion changes when mixing different components. Core math concepts include ratios, algebraic modeling, and equation solving. It utilizes commands like Polygon, Sequence, Textfield, GCD, Segment, and Midpoint, along with objects such as p1, p2, A, B, C, D, poly1, etc. Suitable for high school mathematics teaching to help students understand ratio applications and algebraic problem-solving methods.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → poly1, a, b, d, c
  2. Sequence(A + (B - A) / abs(p1 - p2) * k, k, 1, abs(p1 - p2) - 1) → list1
  3. Sequence(C + (B - A) / abs(p1 - p2) * k, k, 1, abs(p1 - p2) - 1) → list2
  4. Sequence(Segment[Element[list1, k], Element[list2, k]], k, 1, abs(p1 - p2)) → list3
  5. Polygon(A, E, F, C) → poly2, a_1, e, f, c_1
  6. Polygon(E, B, D, F) → poly3, e_1, b_1, d_1, f_1
  7. Sequence(G + (B - A) / abs(p1 - p2) * k, k, 1, abs(p1 - p2) - 1) → list4
  8. Sequence(H + (B - A) / abs(p1 - p2) * k, k, 1, abs(p1 - p2) - 1) → list5
  9. Sequence(Segment[Element[list4, k], Element[list5, k]], k, 1, abs(p1 - p2)) → list6
  10. Polygon(G, K, L, H) → poly4, g, k, l, h
  11. Polygon(K, I, J, L) → poly5, k_1, i, j, l_1
  12. Textfield(p1) → inputBox1
  13. Textfield(p2) → inputBox2
  14. Textfield(dp) → inputBox3
  15. Textfield(total) → inputBox4
  16. GCD(abs(dp - p1), abs(dp - p2)) → gcd
  17. Sequence(G + (B - A) / abs(p1 - p2) * gcd * k, k, 1, abs(p1 - p2) / gcd - 1) → list7
  18. Sequence(H + (B - A) / abs(p1 - p2) * gcd * k, k, 1, abs(p1 - p2) / gcd - 1) → list8
  19. Sequence(Segment[Element[list7, k], Element[list8, k]], k, 1, abs(p1 - p2)) → list9
  20. Textfield(p1) → inputBox5
  21. Textfield(p2) → inputBox6
  22. Textfield(dp) → inputBox7
  23. Segment(M, N) → p
  24. GCD(100 * abs(dp - p1), 100 * abs(dp - p2)) → gcd2
  25. Textfield(text9) → inputBox8
  26. Midpoint(H, L) → O
  27. Midpoint(L, J) → P