1. v = 80km/h t = 1h + 45/60 h = 1,75 h d = v·t = 80·1,75 = 140km
2. (3x+2)/(2x+1) ∈ Z ⇔ (2x+1) | (3x+2)
daca d | (3x+2) ⇒ d | 2(3x+2) = 6x + 4 (1)
si d | (2x+1) ⇒ d | 3(2x+1) = 6x + 3 (2)
⇒ d | [(1) - (2) = 1] ⇒ d ∈ {-1;1}
2x+1 = - 1 2x = -2 x = -1
2x + 1 = 1 2x = 0 x = 0 ⇒ x ∈ {-1,0}
3. (x-1)/4 = y/5 = (z+1)/7 = k x-1 = 4k x = 4k + 1 ; y = 5k ;
z+1= 7k z = 7k - 1
(x+y+z)/3 = 16 x+ y+z = 48 4k+1+5k+7k-1 = 48 16k = 48 k = 3
x = 13; y = 15 ; z = 20
