Question

Dacă numerele naturale a, b, c, d verifică condiţiile: 2a = 3b, 5b = 4c, 2c = 5d să se determine a, b, c, d ştiind că: 2a + 3b + 4c - 5d = 136;​

Answer 1

Răspuns:

2a=3b

5b=4c

2c=5d

a=3b/2

c=5b/4

2c=5d|·2=>4c=10d=>5b=4c=>5b=10d=>b=2d=>d=b/2

2a+3b+4c-5d=136

2·3b/2+3b+4·5b/4-5b/2=136

3b+3b+5b-5b/2=136

11b-5b/2=136

22b-5b=272=>17b=272=>b=16

2a=3·16=>2a=48=>a=24

5·16=4c=>c=20

d=b/2=>d=8

V:2·24+3·16+4·20-5·8=48+48+80-40=136

Answer 2

Răspuns:

Explicație pas cu pas:

2a = 3b

        5b = 4c

                 2c = 5d =>   5d = 5b/2

_________________

2a + 3b + 4c - 5d = 136

↓       ↓      ↓     ↓

3b + 3b + 5b - 5 b/2 = 136 l x 2  

22b - 5 b = 2 x 136

17 b = 272

b = 272 : 17    =>    b = 16

a = 3 x b : 2 =>   a = 3 x 16 : 2  =>   a = 24

c = 5 x b : 4 =>   c = 5 x 16 : 4  =>   c = 20

d = 2 x c : 5 =>   d = 2 x 20 : 5  =>  d = 8

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Verific:  2 x 24 + 3 x 16 + 4 x 20 - 5 x 8 = 48 + 48 + 80 - 40 = 136