Question Number 76991 by liki last updated on 02/Jan/20
Commented by liki last updated on 02/Jan/20
$$....\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:\boldsymbol{{plz}}. \\ $$
Answered by MJS last updated on 02/Jan/20
![we have p people, everybody gets ((432)/p) oranges with p−4 people everybody gets ((432)/p)+9 ⇒ ((432)/(p−4))=((432)/p)+9 ((432)/(p−4))=((9p+432)/p) ∣×p(p−4) 432p=(9p+432)(p−4) 432p=9p^2 +396p−1728 9p^2 −36p−1728=0 p^2 −4p−192=0 ⇒ p=−12 [not useable] or p=16 ⇒ 16 people](Q76994.png)
$$\mathrm{we}\:\mathrm{have}\:{p}\:\mathrm{people},\:\mathrm{everybody}\:\mathrm{gets}\:\frac{\mathrm{432}}{{p}}\:\mathrm{oranges} \\ $$$$\mathrm{with}\:{p}−\mathrm{4}\:\mathrm{people}\:\mathrm{everybody}\:\mathrm{gets}\:\frac{\mathrm{432}}{{p}}+\mathrm{9} \\ $$$$\Rightarrow \\ $$$$\frac{\mathrm{432}}{{p}−\mathrm{4}}=\frac{\mathrm{432}}{{p}}+\mathrm{9} \\ $$$$\frac{\mathrm{432}}{{p}−\mathrm{4}}=\frac{\mathrm{9}{p}+\mathrm{432}}{{p}}\:\:\:\:\:\mid×{p}\left({p}−\mathrm{4}\right) \\ $$$$\mathrm{432}{p}=\left(\mathrm{9}{p}+\mathrm{432}\right)\left({p}−\mathrm{4}\right) \\ $$$$\mathrm{432}{p}=\mathrm{9}{p}^{\mathrm{2}} +\mathrm{396}{p}−\mathrm{1728} \\ $$$$\mathrm{9}{p}^{\mathrm{2}} −\mathrm{36}{p}−\mathrm{1728}=\mathrm{0} \\ $$$${p}^{\mathrm{2}} −\mathrm{4}{p}−\mathrm{192}=\mathrm{0} \\ $$$$\Rightarrow\:{p}=−\mathrm{12}\:\left[\mathrm{not}\:\mathrm{useable}\right]\:\mathrm{or}\:{p}=\mathrm{16} \\ $$$$\Rightarrow\:\mathrm{16}\:\mathrm{people} \\ $$
Commented by liki last updated on 02/Jan/20
$$..\boldsymbol{{thank}}\:\boldsymbol{{you}}\:\boldsymbol{{sir}}. \\ $$