Question

Determinati nr a,b stiind ca sunt direct proportionale cu 5,8, iar diferenta lor este egala cu 45.

Answer 1

$\it a,\ \ b \in\mathbb{N},\ b > a,\ \ b-a=45 \Rightarrow b=45+a\ \ \ \ \ \ (1)\\ \\ \{a,\ \ b\}\ d.\ p.\ \{5,\ \ 8\} \Rightarrow \dfrac{a}{5}=\dfrac{b}{8} \stackrel{(1)}{\Longrightarrow} \dfrac{a}{5}=\dfrac{45+a}{8} \Rightarrow 8a=225+5a\bigg|_{-5a} \Rightarrow \\ \\ \\ \Rightarrow 3a=225\bigg|_{:3} \Rightarrow a=75\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow b=45+75 \Rightarrow b=120$

Answer 2

Explicație pas cu pas:

proporții derivare:

a < b

$\dfrac{a}{5} = \dfrac{b}{8} = \dfrac{b - a}{8 - 5} = \dfrac{45}{3} = 15$

$\dfrac{a}{5} = 15 \iff a = 5 \times 15 \implies a = 75$

$\dfrac{b}{8} = 15 \iff b = 8 \times 15 \implies b = 120$