Question

100 de puncte, 15,16 si 18 va rog

Answer 1

15. a/b = 7/3
   a) a+b = 140, adica a = 140-b
     (140-b)/b = 7/3
     3(140-b) = 7b
     420 - 3b = 7b
     420 = 10b
    b = 420/10 = 42
    a= 140-42 = 98

   b) a-b = 140
      a = 140+b
     (140+b)/b = 7/3
     3(140+b) = 7b
     420 + 3b = 7b
     420 = 4b
     b = 105
     a = 140+105 = 245

c) a+b = 280
    a = 280-b
    (280-b)/b = 7/3
    3(280-b) = 7b
    840 - 3b = 7b
    10b = 840
    b = 84
    a = 280-84 = 196

d) a-b = 56 => a = 56+b
    (56+b)/b = 7/3
    3(56+b) = 7b => 168+3b = 7b => 4b = 168
    b = 42
    a = 56+42 = 98

e) a+2b = 260 => a = 260-2b
   (260-2b)/b = 7/3 => 3(260-2b) = 7b => 780 - 6b = 7b => 13b = 780
   b = 60
   a = 260-2*60 = 140

f) 3a+b = 120 => b = 120-3a
  a/(120-3a ) = 7/3
  3a = 7(120-3a)
  3a = 840 - 21a
  24a = 840
  a = 35
  b = 120-3*35 = 15

16.a) 2a/b = 3/4
        a/b = 3/4:2 = 3/4 x 1/2 = 3/8
     b) 3a/2b = 1
        a/b = 1: 3/2 = 1x2/3 = 2/3
     c) 5a/2b = 20
        a/b = 20 : 5/2 = 20 x 2/5 = 8
     d) 7a/5b = 49/15
        a/b = 49/15 : 7/5 = 49/15 x 5/7 = 7/3
     e) 4a/3b = 32/15
        a/b = 32/15 : 4/3 = 32/15 x 3/4 = 8/5
     f) 8a/5b = 16/35
       a/b = 16/35 : 8/5 = 16/35 x 5/8 = 2/7

18. a/b = 4/3
   a) (a+b)/(a-b) = (a/b + b/b)/(a/b - b/b) = (4/3 + 1)/(4/3-1) = (7/3)/(1/3) = 7/3 x 3/1 = 7
   b) (a+b)/(3a-b) = (a/b+b/b)/(3a/b - b/b) = (4/3+1)/(3*4/3-1) = (7/3)/3 = 7/3 x 1/3 = 7/9
   c) (3a+2b)/(a-b) = (3a/b+2b/b)/(a/b - b/b) = (3*4/3+2)/(4/3-1) = 6/(1/3) = 6 x 3/1 = 18
   d) (3a+7b)/(8a-b) = (3a/b + 7b/b)/(8a/b - b/b) = (3*4/3 + 7)/(8*4/3 - 1) = 11/(32/3 - 3/3) = 11/(29/3) = 11 x 3/29 = 33/29
   e) (5a-6b)/(6a-4b) = (5a/b - 6b/b)/(6a/b - 4b/b) = (5*4/3-6)/(6*4/3-4) = (20/3-18/3)/(24/3-12/3) = (2/3)/(12/3) = (2/3)/4 = 2/3 x 1/4 = 1/6
   f) (a^2 + b^2)/5ab = (a^2/b^2 + b^2/b^2)/(5ab/b^2) = [(4/3)^2+1]/(5*4/3) = (16/9+1)/(20/3) = (25/9)/(20/3) = 25/9 x 3/20 = 5/12