Question

Determinati 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) a/11= b/8=k
a=11k
b=8k

a+b=76
11k+8k=76
19k=76
k=4

a=11*4=44
b=8*4=32

b)a-b=0,9
11k-8k=0,9
3k=0,9
k= 0,3

a=11*0,3=3,3
b=8*0,3= 2,4

c)3a+b=41
3*11k+4k=41
33k+4k=41
37k=41
k=1,108

a=11*1,108=12,189
b=4*1,108=4,432

Answer 2

a/11=b/8
Inmultim pe diagonala si este
8a=11b
a=11b/8

a)a+b=76
11b/8+b=76
(11b+8b)/8=76
19b=76*8
19b=608
b=608/19
b=32
a+b=76
a+32=76
a=76-32
a=44

b)a-b=0.9
11b/8-b=0.9
(11b-8b)/8=0.9
3b=0.9*8
3b=7.2
b=7.2/3
b=2.4
a-b=0.9
a-2.4=0.9
a=0.9+2.4
a=3.3

c)3a+b=41
3(11b/8)+b=41
33b/8+b=41
41b/8=41
41b=41*8
41b=328
b=328/41
b=8
3a+b=41
3a+8=41
3a=41-8
3a=33
a=33/3
a=11