Question Number 68285 by mezihloic last updated on 08/Sep/19
![two students ngum ebon gave their ages as 124_4 and 33_x respectively.if both of them are of thesame ages .find in what base ebon gave her age](https://www.tinkutara.com/question/Q68285.png)
$${two}\:{students}\:{ngum}\:{ebon}\:{gave}\:{their}\:{ages}\:{as}\:\mathrm{124}_{\mathrm{4}} {and}\:\mathrm{33}_{{x}} {respectively}.{if}\:{both}\:{of}\:{them}\:{are}\:{of}\:{thesame}\:{ages}\:.{find}\:{in}\:{what}\:{base}\:{ebon}\:{gave}\:{her}\:{age} \\ $$
Commented by Rasheed.Sindhi last updated on 08/Sep/19
![124_4 ? A number written in the base of 4 must be composed of only 0,1,2,3](https://www.tinkutara.com/question/Q68290.png)
$$\mathrm{124}_{\mathrm{4}} ? \\ $$$$\mathrm{A}\:\mathrm{number}\:\mathrm{written}\:\mathrm{in}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{4} \\ $$$$\mathrm{must}\:\mathrm{be}\:\mathrm{composed}\:\mathrm{of}\:\mathrm{only}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3} \\ $$
Commented by Rasheed.Sindhi last updated on 08/Sep/19
![If it were as: age of ngum=123_4 & age of ebon=33_x 3x+3=1(4)^2 +2(4)+3 3x=24 x=((24)/3)=8](https://www.tinkutara.com/question/Q68292.png)
$$\mathrm{If}\:\mathrm{it}\:\mathrm{were}\:\mathrm{as}: \\ $$$$\mathrm{age}\:\mathrm{of}\:\mathrm{ngum}=\mathrm{123}_{\mathrm{4}} \:\&\:\mathrm{age}\:\mathrm{of}\:\mathrm{ebon}=\mathrm{33}_{\mathrm{x}} \\ $$$$\:\:\:\:\:\:\mathrm{3x}+\mathrm{3}=\mathrm{1}\left(\mathrm{4}\right)^{\mathrm{2}} +\mathrm{2}\left(\mathrm{4}\right)+\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{3x}=\mathrm{24} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\frac{\mathrm{24}}{\mathrm{3}}=\mathrm{8} \\ $$
Answered by $@ty@m123 last updated on 08/Sep/19
![1×4^2 +2×4+4=3x+3 28=3x+3 3x=25 x=((25)/3)](https://www.tinkutara.com/question/Q68288.png)
$$\mathrm{1}×\mathrm{4}^{\mathrm{2}} +\mathrm{2}×\mathrm{4}+\mathrm{4}=\mathrm{3}{x}+\mathrm{3} \\ $$$$\mathrm{28}=\mathrm{3}{x}+\mathrm{3} \\ $$$$\mathrm{3}{x}=\mathrm{25} \\ $$$${x}=\frac{\mathrm{25}}{\mathrm{3}} \\ $$