Question-180490

Question Number 180490 by Shrinava last updated on 12/Nov/22

Answered by a.lgnaoui last updated on 13/Nov/22

m=60%M=Masse(final) m+x x=masse sugar 76%(60%M+x)+x=100%M 76(60%M+x)=100M 76×60%M+76x+x=100M x=((100−(76×60)%)/(77))=((100−45,60)/(77))=((53,4)/(77))=0,7/ kg ?

$${m}=\mathrm{60\%}{M}={Masse}\left({final}\right) \\ $$$${m}+{x}\:\:\:\:\:{x}={masse}\:{sugar} \\ $$$$\mathrm{76\%}\left(\mathrm{60\%}{M}+{x}\right)+{x}=\mathrm{100\%}{M} \\ $$$$\mathrm{76}\left(\mathrm{60\%}{M}+{x}\right)=\mathrm{100}{M} \\ $$$$\mathrm{76}×\mathrm{60\%}{M}+\mathrm{76}{x}+{x}=\mathrm{100}{M} \\ $$$${x}=\frac{\mathrm{100}−\left(\mathrm{76}×\mathrm{60}\right)\%}{\mathrm{77}}=\frac{\mathrm{100}−\mathrm{45},\mathrm{60}}{\mathrm{77}}=\frac{\mathrm{53},\mathrm{4}}{\mathrm{77}}=\mathrm{0},\mathrm{7}/\:\:{kg}\:? \\ $$$$ \\ $$

Commented by Shrinava last updated on 13/Nov/22

Dear professor, Answers: a)8 b)18 c)10 d)24 e)36

$$\mathrm{Dear}\:\mathrm{professor}, \\ $$$$\left.\mathrm{A}\left.\mathrm{n}\left.\mathrm{s}\left.\mathrm{w}\left.\mathrm{ers}:\:\:\mathrm{a}\right)\mathrm{8}\:\:\mathrm{b}\right)\mathrm{18}\:\:\mathrm{c}\right)\mathrm{10}\:\:\mathrm{d}\right)\mathrm{24}\:\:\mathrm{e}\right)\mathrm{36} \\ $$

Answered by mr W last updated on 13/Nov/22

Behmez =b kg Sugar added =s kg mass of sugar is 24% of mass of behmez in final product. s=0.24×0.6b=0.144b=((18b)/(125)) s, b are integer. ⇒b=125k, s=18k with k∈N that means at least 125 kg behmez and at least 18 kg sugar.

$${Behmez}\:={b}\:{kg} \\ $$$${Sugar}\:{added}\:={s}\:{kg} \\ $$$${mass}\:{of}\:{sugar}\:{is}\:\mathrm{24\%}\:{of}\:{mass}\:{of}\: \\ $$$${behmez}\:{in}\:{final}\:{product}. \\ $$$${s}=\mathrm{0}.\mathrm{24}×\mathrm{0}.\mathrm{6}{b}=\mathrm{0}.\mathrm{144}{b}=\frac{\mathrm{18}{b}}{\mathrm{125}} \\ $$$${s},\:{b}\:{are}\:{integer}. \\ $$$$\Rightarrow{b}=\mathrm{125}{k},\:{s}=\mathrm{18}{k}\:{with}\:{k}\in\mathbb{N} \\ $$$${that}\:{means}\:{at}\:{least}\:\mathrm{125}\:{kg}\:{behmez}\: \\ $$$${and}\:{at}\:{least}\:\mathrm{18}\:{kg}\:{sugar}. \\ $$

Commented by Shrinava last updated on 17/Nov/22