Question

Scrieti numarul 394 ca suma de 4 termeni astfel incat:
a/b=0,625/0,75
d/c=1,(1)/0,(6)
a/d=7,5/2
REPEDE

Answer 1

0,625=625/1000=5/8
0,75=75/100=3/4
=>a/b=5/8 x 4/3 = 5/6 =>a/5=b/6

1,(1)= 1 intreg 1/9 = 10/9
0,(6)= 6/9 = 2/3
=>d/c=10/9 x 3/2 = 5/3 =>d/5=c/3

7,5=75/10=15/2
=>a/d=15/2 x 1/2 = 15/4 =>a/15=d/4

a/5=b/6 Daca inmultim cu 1/3 avem a/15=b/18 =>d/4=b/18 sau d/2=b/9
d/5=c/3
a/15=d/4
a+b+c+d=394
Incercam sa le exprimam pe toate in functie de o singura litera.
a=5b/6
d=2b/9
c=3d/5=(3x2b/9)/5=2b/15
5b/6 + b + 2b/15 + 2b/9 = 394
Numitor comun 
6=2x3
15=3x5
9=3²
_______
c.m.m.m.c.=2x3²x5=90
75b+90b+12b+20b=35460
197b=35460 =>b=180
=>a=5b/6=150
=>c=2b/15=24
=>d=2b/9=40