Question

Va rog mult , 16 puncte dau , rod pls....1 . Aflati numerele a,b,c ∈ Ф+, stiind ca sunt direct proportionale cu numerele
a) 2; 3 ; 6 si a = 4
b) 4 ; 0,(5) ; 0,6 si b = 10
c) 6 ; 1,2 ; 3 supra 5 si c = 0,6
d) 4 ; 6 ; 5 si a + b = 30

2.Determinati x,y,z ∈ Ф+ stiin ca ele sunt direct proportionale cu numerele :
a) 3 ; 4 ; 8 si k = 2
b)5 ; 1,5 ; 4 si k = 0,2
c) 1 supra 2 ; 0,(4) ; 6 si k = 1 supra 8
d) 0,3 ; 9,(6) ; 3 supra 8 si k = 0,2(1)

Answer 1

a) a/2=b/3=c/6 = k
a/2=k, a = 2*k, 4 = 2*k, k = 4:2, k = 2
b/3 = k, b = 3*k, b = 3*2, b = 6
c/6 = k,c = 6*k, c = 6*2, c = 12
b)a/4=9b/5=10c/6 = k
    a/4 = k,a= 4*k, a = 4*18, a = 72
    9b/5 = k,9b = 5*k, 9*10 = 5*k, 90=5*k, k = 90:5,  k =18
    10c/6 = k, 10c =6*k, 10c = 6*18, 10c = 108, c = 108/10, c = 10,8
c) a/6=b/12=5c/3=k
     a/6 = k. a = 6k, a = 6*5, a = 30
     b/12 = k, b = 12k, b = 12*5, b = 60
     5c/3 = k, c = 3k, 0,6 = 3k, 6/10=3k, 30k = 6, k = 30:6, k = 5
d) a/4=b/6=c/5 = k
    a/4 = k, a = 4k, a = 4*3 = 12
    b/6 = k, b = 6k, b = 6*3 = 18
    c/5 = k, c = 5k, c = 5*3 = 15
a+b = 30, 4k+6k = 30, 10k = 30, k = 30:10, k = 3

2.
a) a/3=b/4=c/8 = k
a/3 = b/4 = c/8 = 2
a/3 = 2, a = 3*2 = 6
b/4 = 2, b = 4*2 = 8
c/8 = 2, c = 8*2 = 16
b) a/5=b/15=c/4 = k
a/5 = b/15 = c/4 = 0,2
a/5 = 0,2, a = 5*0,2 = 1
b/15 = 0,2, b = 15*0,2 = 3
c/4 =0,2, c = 4*0,2 = 0,8
c) a/1/2 = b/4/9 = c/6 = k
 a/1/2=b/4/9=c/6 = 1/8
a/1/2=1/8, a/1:1/2 = 1/8 a/1*2/1 = 1/8, 2a = 1/8, 2a/1 = 1/8, 16a = 1, a = 16/1, a = 16
b/4/9=1/8, b/1:4/9=1/8, b/1*9/4 =1/8, 9b/4 = 1/8, 72b =4, b = 72:4, b = 18
c/6 = 1/8, 8c = 6, c = 8/6, c = 4/3, c = 1,(3)
d) pe ultimul nu il stiu
imi pare rau