Question

Demonstrati numerele a si b stiind ca a/11=b/8 si : a) a+b=76 b) a-b=0,9 c) 3a+b=41

Answer 1

a/11=b/8, a=11b/8
a)a+b=76
(11b/8)+b=76
11b+8b=608
19b=608, b=608/19=32, a=76-32=44
b)a-b=0,9
11b/8-b=0,9, 11b-8b=7,2, 3b=7,2, b=7,2/3=2,4
a=b+0,9=2,4+0,9=3,3
c)3a+b=41, 3*11b/8+b=41, 33b+8b=328,41b=328, b=328/41=8
3a+8=41, 3a=33, a=11

Answer 2

a / 11 = b / 8 = K

a / 11 = K => a  = 11 K
b / 8 = K => b = 8 K
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a ) a + b = 76

⇒ 11 K + 8 K = 76

19 K = 76

K = 76 : 19

K = 4

a = 4 x 11 = 44

b = 4 x 8 = 32

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b ) a - b = 0,9

11 K - 8 K = 0,9

3 K = 0,9

K = 0,9 : 3

K  = 0,3

a  = 0,3 x 11 = 3,3

b = 0,3 x 8  = 2,4

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c ) 3a  + b = 41

3 x 11 K +  4  K = 41

33 K + 4 K  = 41

37 K = 41

K = 41 : 37

K = 1,108

a = 1,108 x 11 = 12,189

b = 1,108 x 4 = 4,432

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