Question

stiind ca 3a supra 2b = 5 supra 4 , 3b supra 5c = 6 supra 7 si a+b+c=1672 aflati a,b si c​

Answer 1

3a/2b = 5/4 => a/b × 3/2 = 5/4 => a/b = (5/4) : (3/2) = 5/4 × 2/3 = 5/2 × 1/3 = 5/6

a/b = 5/6

3b/5c = 6/7 => b/c × 3/5 = 6/7 => b/c = (6/7) : (3/5) = 6/7 × 5/3 = 2/7 × 5/1 = 10/7 =>

c/b = 7/10

a + b + c = 1672

Împărțim această relatie prin b si obtinem:

a/b + b/b + c/b = 1672/b

5/6 + 1 + 7/10 = 1672/b

50/60 + 60/60 + 42/60 = 1672/b

152/60 = 1672/b

38/15 = 1672/b

38b = 1672 × 15

b = 1672×15/38 = 44×15 = 660

b = 660

Dar a/b = 5/6 => 6a = 5b = 5×660 =>

a = 5×660/6 = 5×110/1

a = 550

c/b = 7/10 => 10c = 7b = 7×660 =>

c = 7×660/10 = 7×66/1

c = 462

R: a = 550, b = 660, c = 462