Răspuns:
a = 6
b = 15
c = 10
d = 20
Explicație pas cu pas:
0,2 = 2/10 = 1/5
0,5 = 5/10 = 1/2
0,(3) = 3/9 = 1/3
0,(6) = 6/9 = 2/3
[a, b, c, d] d.p. [0,2; 0,5; 0,(6); 0,(9)]
a/(1/5) = b/(1/2) = c/(1/3) = d/(2/3) = > k
a = k/5
b = k/2
c = k/3
d = 2k/3
3a - c + d - b = 13
3k/5 - k/3 + 2k/3 - k/2 = 13
3k/5 + k/3 - k/2 = 13 / x30
18k + 10k - 15k = 390
13k = 390
k = 390 : 13
k = 30
a = k/5 = 30/5 = 6
b = k/2 = 30/2 = 15
c = k/3 = 30/3 = 10
d = 2k/3 = 60/3 = 20
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