Question

Determinati numerele x,y si z invers proportionale cu numerele1, 1,(3) 1,1(6) si 1,8(3) daca x+y-3z=135! Va rog mult, dar vreau rezolvari de clasa a 7 a!!!

Answer 1

{ X, Y, Z } i.p { 1,1(3); 1,1(6); 1,8(3) }
1,1(3) = 113-11/90 = 102/90 = 17/15
1,1(6) = 116-11/90 = 105/90 = 7/6
1,8(3) = 183-18/90 = 165/90 = 11/6

X x 17/15 = Y x 7/6 = Z x 11/6 = k
X x 17/15 = k ⇒ X = 15k/17
Y x 7/6 = k ⇒ Y = 6k/7
Z x 11/6 = k ⇒ Z = 6k/11
X + Y + 3Z = 135
77)        187)    119)
15k/17 + 6k/7 - 18k/11 = 135
1125k/1309 + 1122k/1309 - 2142k/1309 = 135
105k/1309 = 135
105k = 135 x 1309
105k = 137445
k = 1309
X = 15x1309 / 17 = 1155
Y = 6x1309 / 7 = 1122
Z = 6x1309 / 11 = 714