Bạn tham khảo!
$\dfrac{x}{3}$ $=$ $\dfrac{y}{4}$ $;$ $\dfrac{y}{5}$ $=$ $\dfrac{z}{7}$ và $2x$ $+$ $3y$ $-$ $z$ $=$ $186$
Ta có : $\dfrac{x}{3}$ $=$ $\dfrac{y}{4}$ $→$ $\dfrac{x}{3}$ $.$ $\dfrac{1}{5}$ $=$ $\dfrac{y}{4}$ $.$ $\dfrac{1}{5}$
$→$ $\dfrac{x}{15}$ $=$ $\dfrac{y}{20}$ (1)
Ta có : $\dfrac{y}{5}$ $=$ $\dfrac{z}{7}$ $→$ $\dfrac{y}{5}$ $.$ $\dfrac{1}{4}$ $=$ $\dfrac{z}{7}$ $.$ $\dfrac{1}{4}$
$→$ $\dfrac{y}{20}$ $=$ $\dfrac{z}{28}$ (2)
Từ (1) và (2) $→$ $\dfrac{x}{15}$ $=$ $\dfrac{y}{20}$ $=$ $\dfrac{z}{28}$
$→$ $\dfrac{2x}{30}$ $=$ $\dfrac{3y}{60}$ $=$ $\dfrac{z}{28}$
Áp dụng t/c dãy tỉ số $=$ nhau ta có :
$\dfrac{2x}{30}$ $=$ $\dfrac{3y}{60}$ $=$ $\dfrac{z}{28}$ $=$ $\dfrac{2x+3y-z}{30+60-28}$ $=$ $\dfrac{186}{62}$ $=$ $3$
$→$ $\dfrac{2x}{30}$ $=$ $3$ $→$ $2x$ $=$ $30$ $.$ $3$ $→$ $2x$ $=$ $90$ $→$ $x$ $=$ $90$ $:$ $2$ $=$ $45$
và $\dfrac{3y}{60}$ $=$ $3$ $→$ $3y$ $=$ $60$ $.$ $3$ $→$ $3y$ $=$ $180$ $→$ $y$ $=$ $180$ $:$ $3$ $=$ $60$
và $\dfrac{z}{28}$ $=$ $3$ $→$ $z$ $=$ $28$ $.$ $3$ $=$ $84$
$FbBinhne2k88$
