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Question Number 105006 by mathocean1 last updated on 25/Jul/20

Miranda did market in 3 day. The monday, she bought 3kg of fish^� ,2kg of meat ,1kg of rice at 10000 $. The wednesday she bought 1kg of fish, 3kg of meat, 2kg of rice at 10000$. And the thursday she bought 4kg of fish, 2kg of meat,3 kg of rice at 12500$. 1) Which price(sum) will spend Miranda if she she go to the market at saturday to buy at the same price 3kg of fish, 1kg of meat and 1.5kg of rice?

$$ \\ $$$${Miranda}\:{did}\:{market}\:{in}\:\mathrm{3}\:{day}. \\ $$$${The}\:{monday},\:{she}\:{bought}\:\mathrm{3}{kg}\:{of}\:{fis}\bar {{h}} \\ $$$$,\mathrm{2}{kg}\:{of}\:{meat}\:,\mathrm{1}{kg}\:{of}\:{rice}\:{at}\:\mathrm{10000}\:\$. \\ $$$${The}\:{wednesday}\:{she}\:{bought}\:\mathrm{1}{kg}\:{of} \\ $$$${fish},\:\mathrm{3}{kg}\:{of}\:{meat},\:\mathrm{2}{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{10000\$}. \\ $$$${And}\:{the}\:{thursday}\:{she}\:{bought}\:\mathrm{4}{kg}\:{of} \\ $$$${fish},\:\mathrm{2}{kg}\:{of}\:{meat},\mathrm{3}\:{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{12500\$}. \\ $$$$\left.\mathrm{1}\right)\:{Which}\:{price}\left({sum}\right)\:{will}\:{spend}\:{Miranda} \\ $$$${if}\:{she}\:{she}\:{go}\:{to}\:{the}\:{market}\:{at} \\ $$$${saturday}\:{to}\:{buy}\:{at}\:{the}\:{same}\:{price} \\ $$$$\mathrm{3}{kg}\:{of}\:{fish},\:\mathrm{1}{kg}\:{of}\:{meat}\:{and}\:\mathrm{1}.\mathrm{5}{kg}\:{of} \\ $$$${rice}? \\ $$

Answered by Rasheed.Sindhi last updated on 25/Jul/20

determinant ((,f,m,r,(sum)),((mon),3,2,1,(10000)),((wed),1,3,2,(10000)),((thu),4,2,3,(12500)),((sat),3,1,(1.5),?)) 3x+2y+ z=10000 x+3y+2z=10000 4x+2y+3z=12500 By Cramer′s rule x=( determinant (((10000),2,1),((10000),3,2),((12500),2,3))_ / determinant ((3,2,1),(1,3,2),(4,2,3))^ ) y=( determinant ((2,(10000),1),(3,(10000),2),(2,(12500),3))_ / determinant ((3,2,1),(1,3,2),(4,2,3))^ ) z=( determinant ((2,1,(10000)),(3,2,(10000)),(2,3,(12500)))_ / determinant ((3,2,1),(1,3,2),(4,2,3))^ )

$$\begin{vmatrix}{}&{{f}}&{{m}}&{{r}}&{{sum}}\\{{mon}}&{\mathrm{3}}&{\mathrm{2}}&{\mathrm{1}}&{\mathrm{10000}}\\{{wed}}&{\mathrm{1}}&{\mathrm{3}}&{\mathrm{2}}&{\mathrm{10000}}\\{{thu}}&{\mathrm{4}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{12500}}\\{{sat}}&{\mathrm{3}}&{\mathrm{1}}&{\mathrm{1}.\mathrm{5}}&{?}\end{vmatrix} \\ $$$$\mathrm{3}{x}+\mathrm{2}{y}+\:\:{z}=\mathrm{10000} \\ $$$$\:\:{x}+\mathrm{3}{y}+\mathrm{2}{z}=\mathrm{10000} \\ $$$$\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{3}{z}=\mathrm{12500} \\ $$$${By}\:{Cramer}'{s}\:{rule} \\ $$$$ \\ $$$${x}=\frac{\begin{vmatrix}{\mathrm{10000}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{10000}}&{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{12500}}&{\mathrm{2}}&{\mathrm{3}}\end{vmatrix}_{} }{\begin{vmatrix}{\mathrm{3}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{2}}&{\mathrm{3}}\end{vmatrix}^{} } \\ $$$$ \\ $$$${y}=\frac{\begin{vmatrix}{\mathrm{2}}&{\mathrm{10000}}&{\mathrm{1}}\\{\mathrm{3}}&{\mathrm{10000}}&{\mathrm{2}}\\{\mathrm{2}}&{\mathrm{12500}}&{\mathrm{3}}\end{vmatrix}_{} }{\begin{vmatrix}{\mathrm{3}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{2}}&{\mathrm{3}}\end{vmatrix}^{} } \\ $$$$ \\ $$$${z}=\frac{\begin{vmatrix}{\mathrm{2}}&{\mathrm{1}}&{\mathrm{10000}}\\{\mathrm{3}}&{\mathrm{2}}&{\mathrm{10000}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{12500}}\end{vmatrix}_{} }{\begin{vmatrix}{\mathrm{3}}&{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{3}}&{\mathrm{2}}\\{\mathrm{4}}&{\mathrm{2}}&{\mathrm{3}}\end{vmatrix}^{} } \\ $$$$ \\ $$

Answered by Rasheed.Sindhi last updated on 25/Jul/20

3x+2y+ z=10000.........(i) x+3y+2z=10000.........(ii) 4x+2y+3z=12500.........(iii) (i)−(ii): 2x−y−z=0⇒z=2x−y ^★ (i)⇒3x+2y+ (2x−y)=10000 ⇒5x+y=10000.........(iv) ^★ (ii)⇒ x+3y+2(2x−y)=10000 ⇒ 5x+y=10000 ^★ (iii)⇒4x+2y+3(2x−y)=12500 ⇒10x−y=12500........(v) (iv)+(v):15x=22500⇒x=1500$ 5x+y=10000⇒y=10000−5(1500) y=2500$ (i)⇒ z=10000−3x−2y (i)⇒ z=10000−3(1500)−2(2500) z=500$ Conclusion:All things are very expensive in mathocean1′s country.

$$\mathrm{3}{x}+\mathrm{2}{y}+\:\:{z}=\mathrm{10000}.........\left({i}\right) \\ $$$$\:\:{x}+\mathrm{3}{y}+\mathrm{2}{z}=\mathrm{10000}.........\left({ii}\right) \\ $$$$\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{3}{z}=\mathrm{12500}.........\left({iii}\right) \\ $$$$\left({i}\right)−\left({ii}\right):\:\mathrm{2}{x}−{y}−{z}=\mathrm{0}\Rightarrow{z}=\mathrm{2}{x}−{y} \\ $$$$ \\ $$$$\:^{\bigstar} \left({i}\right)\Rightarrow\mathrm{3}{x}+\mathrm{2}{y}+\:\left(\mathrm{2}{x}−{y}\right)=\mathrm{10000} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\mathrm{5}{x}+{y}=\mathrm{10000}.........\left({iv}\right) \\ $$$$\:^{\bigstar} \left({ii}\right)\Rightarrow\:{x}+\mathrm{3}{y}+\mathrm{2}\left(\mathrm{2}{x}−{y}\right)=\mathrm{10000} \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\:\mathrm{5}{x}+{y}=\mathrm{10000} \\ $$$$\:^{\bigstar} \left({iii}\right)\Rightarrow\mathrm{4}{x}+\mathrm{2}{y}+\mathrm{3}\left(\mathrm{2}{x}−{y}\right)=\mathrm{12500} \\ $$$$\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{10}{x}−{y}=\mathrm{12500}........\left({v}\right) \\ $$$$\left({iv}\right)+\left({v}\right):\mathrm{15}{x}=\mathrm{22500}\Rightarrow{x}=\mathrm{1500\$} \\ $$$$\mathrm{5}{x}+{y}=\mathrm{10000}\Rightarrow{y}=\mathrm{10000}−\mathrm{5}\left(\mathrm{1500}\right) \\ $$$$\:\:\:\:\:\:\:{y}=\mathrm{2500\$} \\ $$$$\left({i}\right)\Rightarrow\:\:{z}=\mathrm{10000}−\mathrm{3}{x}−\mathrm{2}{y} \\ $$$$\left({i}\right)\Rightarrow\: \\ $$$${z}=\mathrm{10000}−\mathrm{3}\left(\mathrm{1500}\right)−\mathrm{2}\left(\mathrm{2500}\right) \\ $$$${z}=\mathrm{500\$} \\ $$$$\mathrm{Conclusion}:{All}\:{things}\:{are}\:{very} \\ $$$${expensive}\:{in}\:\:{mathocean}\mathrm{1}'{s}\: \\ $$$${country}. \\ $$

Commented by mathocean1 last updated on 25/Jul/20

hahahaha not too expensive ... It is the problem of currency($ instead of XAF) . Thank you sir.

$${hahahaha}\:{not}\:{too}\:{expensive}\:... \\ $$$${It}\:{is}\:{the}\:{problem}\:{of}\:\:{currency}\left(\$\:{instead}\:{of}\:{XAF}\right)\:. \\ $$$${Thank}\:{you}\:{sir}. \\ $$$$ \\ $$

Commented by Rasheed.Sindhi last updated on 26/Jul/20

hahahaha......Amusing information I received(through internet!) I was totally unaware of the currency of your country(XAF).... Anyway you have increased your expences by using $ sign :)

$${hahahaha}......{Amusing} \\ $$$${information}\:{I}\:{received}\left({through}\right. \\ $$$$\left.{internet}!\right)\:{I}\:{was}\:{totally}\:{unaware}\:\:{of}\:{the}\:{currency} \\ $$$${of}\:{your}\:{country}\left({XAF}\right).... \\ $$$${Anyway}\:{you}\:{have}\:{increased} \\ $$$$\left.{your}\:{expences}\:{by}\:{using}\:\$\:{sign}\::\right) \\ $$

Commented by mathocean1 last updated on 25/Jul/20

Exactly sir!

$${Exactly}\:{sir}! \\ $$

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