Question

Daca a supra 2=b supra 5,b supra 3=c supra 4 si a+b+c=410 determinati a,b,c

Answer 1

a/2=b/5 ⇒ a=(2/5)b    (1)

b/3=c/4 ⇒ c = (4/3)b   (2)

a + b + c = 410    (3)

(1), (2), (3) ⇒ (2/5)b  + b + (4/3)b = 410 ⇒ b(2/5 + 1 + 4/3) = 410 ⇒

⇒ b·(41/15) = 410 ⇒ b =410·(15/41) ⇒ b = 150    (4)

(1), (4) ⇒ a = (2/5)·150 ⇒ a = 60

(2), (4) ⇒ c = (4/3)· 150 ⇒ c = 200

Deci, numerele cerute sunt:

a= 60,  b=150,  c = 200.

Answer 2

a/2=b/5⇔5a=2b⇔a=2b/5
b/3=c/4⇔3c=4b⇔c=4b/3

a+b+c=410
2b/5+b+4b/3=410⇔6b+15b+20b=410x15⇔ b=150

a=2b/5⇔a=300:5⇔a=60

c=4b/3⇔c=600:3⇔c=200
150+60+200=410