Question

5m de stofa se impart in 4 bucati invers proportionale cu 0,5 ; 0,(3) ; 0,4 si 0,2. Aflati cati metri de stofa are fiecare bucata

Answer 1

a /  1/0,5 = a / 2 
b / 1/0,(3)  = b / 3 
c / 1/0,4  = c / 5/2 = 2c/5
d / 1/0,2 = d / 5 
a+b+c+d = 5
a/2 = b/ 3 ⇒ 3a = 2b ⇒ b= 3a/2
a/2 = 2c/5 ⇒ 5a = 4c ⇒ c = 5a/4
2c/5 = d/5 ⇒ 2c = d ⇒ d= 5a/2
a + 3a/2 + 5a/4 + 5a/2 = 4a+6a+5a+10a / 4 = 25a / 4 = 5 ⇒ 25a = 20 ⇒ 
⇒ a = 4/5 m
b= 6/5 m
c = 1 m
d = 2 m