Question

PLesee help!!
1)Determinati numerele a,b & c direct proportionate cu 0,(3) ; 1,5 ; 1,25 stiindca ca 7A-b+3c=110

2)Determinati numerele a,b&c direct proportionate cu 6,7,9 daca diferenta dintre cel mai mare si cel mai mic numar este egal cu 6

Answer 1

1) { a, b,c } d.p. { 0,(3); 1,5; 1,25 }
   0,(3) = 3/9 = 1/3
  1,5 = 15/10 = 3/2
  1,25 = 125/100 = 5/4
a/ 1/3 = b / 3/2 = c / 5/4 = k
a = 1/3k
b = 3/2k
c = 5/4k
7a - b + 3c = 110
7 x 1/3k - 3/2k + 3 x 5/4k = 110
7/3k - 3/2k + 15/4k = 110
28k - 18k + 45k = 1320
55k = 1320
k = 24
a = 24/3 = 8
b = 3/2 x 24 = 36
c = 5/4 x 24 = 30

2) { a, b, c } d.p. { 6, 7, 9 }
   a/6 = b/7 = c/9 = k
  a = 6k
  b = 7k
  c = 9k
  9k - 6k = 6
  3k = 6
  k = 2
  a = 6 x 2 = 12
  b = 7 x 2 = 14
  c = 9 x 2 = 18