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determinati numerele a si b stiind ca a supra 11 = b supra 8 si:

a) a+b=76 b)a - b=0,9 c)3a + b=41


Răspuns :

a)

a/11 = b/8 => a=11b/8

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

(amplificăm b si 76 cu 8)

=> 11b/8 + 8b/8 =608/8

=> 11b+8b=608=>19b=608=>b=608:19=>b=32

a=76-b=>a=76-32=>a=44

b)a-b=0,9

=> 11b/8 - b=0,9

=>11b/8 - b =9/10

(amplificăm 11b/8 cu 5, b cu 40 si 9/10 cu 4)

=>55b/40 - 40b/40 =36/40

=> 55b-40b= 36

=> 15b=36 => b=36:15=>b=2,4

a=0,9+2,4=>a=3,3

c)3a+b=41=>

3×11b/8+b=41=>

33b/8+b=41=>

(amplificam pe b si 41 cu 8)

=> 33b/8 + 8b/8 =41/8

=> 33b+8b=41

=> 41b=41=> b=1

a=11×b/8=>a=11/8