33. (6a + b)/(5a + 2b) = 8/10
Impartim atat numaratorul, cat si numitorul fractiei din stanga prin b.
(6a/b + b/b)/(5a/b + 2b/b) = 8/10
(6a/b + 1)/(5a/b + 2) = 8/10
(6a/b + 1) * 10 = 8 * (5a/b + 2)
60a/b + 10 = 40a/b + 16
60a/b - 40a/b = 16 - 10
20a/b = 6
a/b = 6/20 = 3/10
34. (5a + 7b)/(2a+11b) = 5/3
Impartim prin a:
(5a/a + 7b/a)/(2a/a + 11b/a) = 5/3
(5 + 7b/a)/(2 + 11b/a) = 5/3
(5 + 7b/a) * 3 = 5 * (2 + 11b/a)
15 + 21b/a = 10 + 55b/a
15 - 10 = 55b/a - 21b/a
5 = 34b/a
b/a = 5/34
32. (14a - 4b)/3a + 7b) = 6/7
(14a/b - 4b/b)/(3a/b + 7b/b) = 6/7
(14a/b - 4)/(3a/b + 7) = 6/7
(14a/b - 4) * 7 = 6 * (3a/b + 7)
98a/b - 28 = 18a/b + 42
98a/b - 18a/b = 42 + 28
80a/b = 70
a/b = 70/80 = 7/8
35. (a - 2)/3 = 5/(b-1)
(a-2)(b-1) = 5*3 = 15
Varianta 1: a-2 = 1 => a = 3, b-1 = 15 => b = 16
Varianta 2: a-2 = 3 => a = 5, b-1 = 5 => b = 6
Varianta 3: a-2 = 5 => a = 7, b-1 = 3 => b = 4
Varianta 4: a-2 = 15 => a = 17, b-1 = 1 => b = 2
