a)\(\left|x+\dfrac{1}{5}\right|=7,5+24\\
\Rightarrow x+\dfrac{1}{5}=7,5+24\\
x+\dfrac{1}{5}=31,5\\
x=31,5-\dfrac{1}{5}\\
x=31,1\)
b)\(\dfrac{x}{15}=\dfrac{24}{50}\)
\(\dfrac{x}{15}=\dfrac{12}{25}\)
\(\Rightarrow x.25=15.12\\
\dfrac{x.25}{25}=\dfrac{15.12}{25}\\
\rightarrow x=\dfrac{15.12}{25}\\
x=\dfrac{35}{5}\)
c)\(\dfrac{x}{10}=\dfrac{y}{15}\)và y-x=25
áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{y-x}{15-10}=\dfrac{25}{5}=5\)
do đó:
\(\dfrac{x}{10}=5\\
\Rightarrow x=5.10\\
x=50\\
\dfrac{y}{15}=5\\
\Rightarrow y=5.15\\
y=75\)
vậy x=50;y=75
d)\(\dfrac{x}{24}=\dfrac{y}{35}=\dfrac{z}{64}\)và x+y+z=123
áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{x}{24}=\dfrac{y}{35}=\dfrac{z}{64}=\dfrac{x+y+z}{24+35+64}=\dfrac{123}{123}=1\)
do đó:
\(\dfrac{x}{24}=1\\
\Rightarrow x=24\\
\dfrac{y}{35}=1\Rightarrow y=35\\
\dfrac{z}{64}=1\\
\Rightarrow z=64\)
vậy x=24;y=35;z=64
e)\(\dfrac{x}{5}=\dfrac{y}{4}\)và 4x+2y=84
áp dụng t/c dãy tỉ số bằng nhau:
\(\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{4x+2y}{20+8}=\dfrac{84}{28}=3\)
do đó:
\(\dfrac{x}{5}=3\Rightarrow x=3.5\\
x=15\\
\dfrac{y}{4}=3\Rightarrow y=3.4\\
y=12\)
