Question

Cost of 5 tables and 7 chairs is 3350.Cost of 4 tables and 3 chairs is 1900.Find cost of one chair

Answer 1

$\pink{ \underline {\huge \frak{✓ \: Hola! \: Mate \: ✓}}}$
$\\ \\ \underline{ \bf{QUESTION}} : \\ \\ \tiny \bf{Cost \: of \: 5 \: tables \: and \: 7 \: chairs \: is \: 3350. \: Cost \: of \: 4 \: tables \: and \: 3 \: } \\ \tiny \bf{ chairs \: is \: 1900. \: Find \: cost \: of \: one \: chair.} \\ \\ \underline{\bf{FIND}} : \\ \\ \pink{\small\bf{Find \: cost \: of \: one \: chair < < * > > }} \\ \\ \underline{\bf{SOLUTION}} : \\ \\ \blue{\underline{AS \: GIVEN}} : \\ \\ \tiny \bf the \: cost \: of \: 5 \: tables \: and \: 7 \: chairs \: is \: \frak{3350 }\: and \: the \: cost \: 4 \: tables\\ \tiny \bf{and \: 3 \: chairs \: is \: \frak{1900.}} \\ \\ \red {\underline{\small\mathcal{WE \: CAN \: WRITE \: IT \: AS \: FOLLOW }}} : \\ \\ \green{ (i). \: 5x + 7y = 3350.} \\ \\ \green{(ii). \: 4 + 3y = 1900.} \\ \\ \tiny\underline{\bf{Now, we \: have \: to \: arrange \: them \: so, \: first \: of \: all \: multipy \: by \: 4 }} \\ \tiny \underline {\bf{into \: the \: first \: equation \: and \: also \: multiply \: by \: 5 \: in \: second \: equation.}} \\ \\ \tiny \bf{X \rightarrow \: means \: cost \: of \: tables \: and \:Y \rightarrow means \: cost \: of \: chairs } \\ \purple{\underline{\bf{likewise}}} : \\ \\ \bf{ (i).4(5x + 7y = 3350)} \\ \\ \bf{(ii).5(4x + 3y = 1900)} \\ \\ \green{\underline{ \bf{we \: will \: obtain \: these \: equations}}} : \\ \\ \bf (i). 20x + 28y = 13400\\ \bf{(ii). \: 20x + 15y = 9500 } \\ \\ \red{\small{ \underline \mathcal{ON \: SUBSTITUTING \: BOTH \: EQUATIONS}}} \\ \\ \: \: \: \: \: \: \: \: \bf{ \cancel{20x} + 28y = 13400} \\ \: \: \: \: \: \: \: \: \: \bf{ \cancel{20x} + 15y = 9500} \\ \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: - \\ \: \: \: \: \: \: \: \: \: - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{13y = 3900} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{y = \frac{3900}{13} = \pink{\underline{ 300} } } \\ \\ \tiny\underline{ \bf{by \: this \: value \: of \: \: Y \: \: we \: will \: find \: the \: value \: of \: ' X'}} \: \\ \\ \tiny \bf{on \: putting \: the \: value \: of \: y \: in \: given \: first \: equation} \rightarrow \\ \\ > > \bf{(i). \: 5x + 7y = 3350} \\ \\ \bf{ > > \: 5x + 7(300) = 3350} \\ \\ \bf{ > > 5x + 2100 = 3350} \\ \\ \bf{ > > 5x = 3350 - 2100} \\ \\ \bf{ > > 5X = 1250} \\ \\ \bf{ > > X = \frac{ \frak{ \cancel{1250}}}{ \cancel\frak5} } \\ \\ > > \bf{ X =250 } \\ \\ \small \bf{SO, \: the \: cost \: of \: each \: chair \: is \: 300} \:$