Question

suma a patru numere este 5.stiind ca ele sunt invers proportionale cu 1/2;1/3;0,4;0,2 aflati numerele.
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Answer 1

Răspuns:

a = 4/5 ; b = 6/5 ; c = 1 ; d = 2.

Explicație pas cu pas:

a + b + c + d = 5

(a,b,c,d) i.p (1/2;1/3;0,4;0,2)

a x 1/2 = b x 1/3 = c x 2/5 = d x 1/5 = k

a = k : 1/2

a = 2k

b = k : 1/3

b = 3k

c = k : 2/5

c = 5k/2

d = k : 1/5

d = 5k

2k + 3k + 5k/2 + 5k=5  (amplificam cu 2 peste tot)

4k/2 + 6k/2 + 5k/2 + 10k/2 = 10/2

(4k + 6k + 5k + 10k)/2 = 10/2

25k = 10

k = 2/5

a = 2k

a =2 x 2/5

a = 4/5

b = 3k

b = 3*2/5

b = 6/5

c = 5k/2

c = (5 x 2/5)/2

c = (10/5)/2

c = 2/2

c = 1

d=5k

d =5 x 2/5

d =10/5

d = 2