Menu Close

If-x-y-x-y-z-y-z-x-y-z-x-z-x-y-z-p-then-which-of-the-following-can-be-the-value-of-p-




Question Number 8230 by 314159 last updated on 03/Oct/16
If ((x+y)/(x+y+z)) = ((y+z)/(x+y+z)) = ((x+z)/(x+y+z)) =p, then which of  the following can be the value of p?
$$\mathrm{If}\:\frac{{x}+{y}}{{x}+{y}+{z}}\:=\:\frac{{y}+{z}}{{x}+{y}+{z}}\:=\:\frac{{x}+{z}}{{x}+{y}+{z}}\:={p},\:\mathrm{then}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{can}\:\mathrm{be}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{p}? \\ $$
Answered by Rasheed Soomro last updated on 03/Oct/16
(a/A)=(b/B)=(c/C)=((a+b+c)/(A+B+C))   p=((x+y)/(x+y+z)) = ((y+z)/(x+y+z)) = ((x+z)/(x+y+z))        =(((x+y)+(y+z)+(x+z))/((x+y+z)+(x+y+z)+(x+y+z)))         =((2x+2y+2z)/(3(x+y+z)))=((2(x+y+z))/(3(x+y+z)))=(2/3)
$$\frac{\mathrm{a}}{\mathrm{A}}=\frac{\mathrm{b}}{\mathrm{B}}=\frac{\mathrm{c}}{\mathrm{C}}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{A}+\mathrm{B}+\mathrm{C}} \\ $$$$\:\mathrm{p}=\frac{{x}+{y}}{{x}+{y}+{z}}\:=\:\frac{{y}+{z}}{{x}+{y}+{z}}\:=\:\frac{{x}+{z}}{{x}+{y}+{z}} \\ $$$$\:\:\:\:\:\:=\frac{\left(\mathrm{x}+\mathrm{y}\right)+\left(\mathrm{y}+\mathrm{z}\right)+\left(\mathrm{x}+\mathrm{z}\right)}{\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)+\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)+\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)} \\ $$$$\:\:\:\:\:\:\:=\frac{\mathrm{2x}+\mathrm{2y}+\mathrm{2z}}{\mathrm{3}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)}=\frac{\mathrm{2}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)}{\mathrm{3}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right)}=\frac{\mathrm{2}}{\mathrm{3}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *