Question Number 180490 by Shrinava last updated on 12/Nov/22
Answered by a.lgnaoui last updated on 13/Nov/22
$${m}=\mathrm{60\%}{M}={Masse}\left({final}\right) \\ $$$${m}+{x}\:\:\:\:\:{x}={masse}\:{sugar} \\ $$$$\mathrm{76\%}\left(\mathrm{60\%}{M}+{x}\right)+{x}=\mathrm{100\%}{M} \\ $$$$\mathrm{76}\left(\mathrm{60\%}{M}+{x}\right)=\mathrm{100}{M} \\ $$$$\mathrm{76}×\mathrm{60\%}{M}+\mathrm{76}{x}+{x}=\mathrm{100}{M} \\ $$$${x}=\frac{\mathrm{100}−\left(\mathrm{76}×\mathrm{60}\right)\%}{\mathrm{77}}=\frac{\mathrm{100}−\mathrm{45},\mathrm{60}}{\mathrm{77}}=\frac{\mathrm{53},\mathrm{4}}{\mathrm{77}}=\mathrm{0},\mathrm{7}/\:\:{kg}\:? \\ $$$$ \\ $$
Commented by Shrinava last updated on 13/Nov/22
$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\left.\mathrm{A}\left.\mathrm{n}\left.\mathrm{s}\left.\mathrm{w}\left.\mathrm{ers}:\:\:\mathrm{a}\right)\mathrm{8}\:\:\mathrm{b}\right)\mathrm{18}\:\:\mathrm{c}\right)\mathrm{10}\:\:\mathrm{d}\right)\mathrm{24}\:\:\mathrm{e}\right)\mathrm{36} \\ $$
Answered by mr W last updated on 13/Nov/22
$${Behmez}\:={b}\:{kg} \\ $$$${Sugar}\:{added}\:={s}\:{kg} \\ $$$${mass}\:{of}\:{sugar}\:{is}\:\mathrm{24\%}\:{of}\:{mass}\:{of}\: \\ $$$${behmez}\:{in}\:{final}\:{product}. \\ $$$${s}=\mathrm{0}.\mathrm{24}×\mathrm{0}.\mathrm{6}{b}=\mathrm{0}.\mathrm{144}{b}=\frac{\mathrm{18}{b}}{\mathrm{125}} \\ $$$${s},\:{b}\:{are}\:{integer}. \\ $$$$\Rightarrow{b}=\mathrm{125}{k},\:{s}=\mathrm{18}{k}\:{with}\:{k}\in\mathbb{N} \\ $$$${that}\:{means}\:{at}\:{least}\:\mathrm{125}\:{kg}\:{behmez}\: \\ $$$${and}\:{at}\:{least}\:\mathrm{18}\:{kg}\:{sugar}. \\ $$
Commented by Shrinava last updated on 17/Nov/22
$$\mathrm{cool}\:\mathrm{dear}\:\mathrm{professor}\:\mathrm{thank}\:\mathrm{you} \\ $$
Answered by manxsol last updated on 13/Nov/22
