Question

Se considera proportia a = 13.
b 4

Formand proportii derivate,determinati numerele a si b I n fiecare din cazurile :
a) a-b=27
b) a+b=34
c) 5a +2b=365

Multumesc mult <3

Answer 1

a / b = 13 / 4

a - b = 27

a + b = 34

5a + 2b = 365

a / b = 13 / 4

a - b / b = 13 - 4 / 4 = 27 / b = 9/ 4

b = 27 × 4 / 9

b = 12 => a = 27 + 12 = 39

a / b = 13 / 4 => a + b / b = 13 + 4 / 4 => 34/ b = 17 / 4 => b= 34 × 4 / 17

b = 2 × 4 = 8 => a = 34 - 8 = 26

a / b = 13 / 4 => 5a / b = 5 × 13 / 4 => 5a + b / b = 5 × 13 + 8 / 4

=> 365 / b = 73 / b => b = 365 × 4 / 73 = 5 × 4 = 20 => a = 20 × 13 / 4 = 65

Answer 2

a = 13
b     4

a-b = 13-4      ⇒ 27/b = 9/4 ⇒ b= (27 x 4)/9 ⇒ b=12
b          4

a=27+b ⇒ a=27+12 ⇒ a= 39

b) a+b =34
(a+b)/b = (13+4)/4 ⇒ 34/b = 17/4 ⇒ b=(4x34)/17 ⇒ b=8
a=34-b ⇒ a= 34-8 ⇒ a=26
c) 5a+2b = 365
a/b = 13/4 ⇒ a/13 = b/4 = k
a/13=k ⇒ a=13k
b/4=k ⇒ b=4k
5x13k + 2x4k =365 ⇒ 65k + 8k = 365 ⇒73 k = 365 ⇒ k = 365/73⇒k=5
a=13x5 ⇒a= 65
b=4x5 ⇒ b=20