Question

stiind ca 3a/2b=5/4, 3b/5c=6/7 si a+b+c=1672, aflatu a,b si c.
VA ROOOG ESTE URGEEENT!!

Answer 1

Răspuns:

Explicație pas cu pas:

3a/2b=5/4,   a/b = 10/12 = 5/6

3b/5c=6/7,  b/c = 30/21 = 10/7

a/b = 5/6,  (a+b)/b = (5+6)/6, (a+b)/b = 11/6  

b/c = 10/7,  (b+c)/b = (10+7)/7, (b+c)/c = 17/7

Aplicat propr. ale proportiilor

a + b = 11b/6

b+c = 17c/7,  le adunam:

a+b+b+c = 11b/6 + 17c/7

a+b+c = 11b/6 -b + 17c/7

1672 = 5b/6 +17c/7,  dar b = 10c/7

1672 = 50c/6 + 17c/7 = (35c +102c)/42

42*1672 = 152c,   c = 42*11

b= 10*42*11/7 = 10*66

a = 10b/12 = 10*10*66/6 = 50*11