a)x+0,2=31,5
x=31,5-0,2
x= 31,3
b) x:15=24:50
x=(24:50)x15
x=7,2
c)x/10=y/15 ; y-x=25
<=> 15x=10y ;y=x+25
<=> 15x=10.(x+25)
<=> 15x=10x+250
<=> 15x-10x=250
<=> 5x=250
<=> x=50
=> y=50+25
<=> y=75
e)x/5=y/4 d 4x+2y=84
<=> 4x=5y ; 2x+y=42 hay y=42-2x
<=> 4x=5.(42-2x)
<=> 4x=210-10x
<=>10x+4x=210
<=> 14x=210
<=> x=210:14
<=> x=15
=> 15/5=y/4
<=> 3=y/4
=> y=12
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:
\(\dfrac{x}{5}=3\Rightarrow x=3.5\\ x=15\\ \dfrac{y}{4}=3\Rightarrow y=3.4\\ y=12\)
