Question

Numerele rationale a,b,c sunt direct proportionale cu 0,(2), 0,(3),0,(4). Stiind ca c-a=10, determinati valoarea sumei a+2b+c

Answer 1

 a,b,c dp {  0,(2) ; 0,(3) ;  0,(4) } 
0,(2) = 2/9
0,(3) = 3/9=1/3 
0,(4) = 4/9 
2a/9=b/9=4c/9=k 
⇒ a = 2/9k  ; b = 1/3k ; c = 4/9k 
c-a=10
4/9k-2/9k=10
2/9k=10
k=90/2
k=45.

a= 2/9·45 ⇒ a = 10 
b = 1/3 · 45 ⇒ b = 15 
c = 4/9 ·45 ⇒ c = 20
a+2b+c = 10+30+20=60.

Answer 2

0,(2)=2/9
0,(3)=3/9=1/3
0,(4)=4/9

a,b,c   dp  cu  2/9 ;1/3; 4/9

a/2/9=b/1/3=c/4/9=k

a*9/2 = b* 3/1 = c* 9/4=k

9a/2= 3b= 9c/4=k

a=2k/9
b=k/3
c=4k/9

c-a=10

4k/9-2k/9=10
2k/9=10

k=9*10/2=9*5=45

a=2*45/9= 2*5=10
b=45/3=15
c=4*45/9= 4*5=20

a+2b+c= 10+2*15+20= 10+30+20=60