ta có\(\frac{3x}{2}\)=\(\frac{4y}{5}\)=\(\frac{x}{\frac{2}{3}}\)=\(\frac{y}{\frac{5}{4}}\)=k
tadc\(\hept{\begin{cases}x=k.\frac{2}{3}\\y=k.\frac{5}{4}\end{cases}}\)thay vào dk y-x=21
k.\(\frac{5}{4}\)-k.\(\frac{2}{3}\)=k.\(\frac{7}{12}\)=21 => k= 21 : \(\frac{7}{12}\)=36
=> x= 36.\(\frac{2}{3}\)= 24 và y =36.\(\frac{5}{4}\)= 45
\(Từy-x=21\Rightarrow3y-3x=63\)
lại có:\(\frac{3x}{2}=\frac{4y}{5}\Rightarrow3x\times5=2\times4y\left(1\right)\)
Từ 3y-3x=63=>3x=3y-63. Thay vào (1) ta được:
(3y-63)x5=2x4y
<=>15y-315=8y
<=>7y=315
<=>y=45
Thay vào y-x=21 ta cõ x=24
Ta có: 3X/2=4y/5=>3X/2x1/12=4y/5x1/12=>3X/24=4y/60=>x/8=y/15=>y-x/15-8=21/7=3
Do đó:x/8=3=>x=24
y/15=3=>y=45