Question

9 Chairs and 5 tables cost rupees 90 while 5 chairs and 4 tables cost rupees 61. Find the price of 6 chairs and 3 tables.​

Answer 1

Costof6chairsand5tables=57rupees

\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}

Step−by−stepexplanation:

• In the given question information given about 9 Chairs and 5 tables cost rupees 90 while 5 chairs and 4 tables cost rupees 61.

• We have to Find the price of 6 chairs and 3 tables.

\begin{gathered} \text{let\:Assuming : } \\ :\implies \text{Let \: Cost \: of \: one \: chair = c} \\ \\ :\implies\text{Cost \: of \: one \: table= t}\\ \\ \green{\underline \bold{Given : }} \\ :\implies 9c + 5t = 90 \\ \\ :\implies 5c + 4t = 61 \\ \\ \red{\underline \bold{To \: Find : }} \\ :\implies Cost \: of \: 6 \: chair = ? \\ \\ :\implies Cost \: of \: 3 \: tables = ?\end{gathered}

letAssuming :

:⟹Let Cost of one chair = c

:⟹Cost of one table= t

Given:

:⟹9c+5t=90

:⟹5c+4t=61

ToFind:

:⟹Costof6chair=?

:⟹Costof3tables=?

• According to given question :

\begin{gathered} :\implies 9c + 5t = 90 - - - - - (1) \\ \\ :\implies 5c + 4t = 61 - - - - - (2) \\ \\ \bold{Using \: substitution \: method : } \\ \\ \bold{On \: solving \: (1) \: we \: get \to} \\ :\implies 9c = 90 - 5t \\ \\ :\implies c = \frac{90 - 5t}{9} - - - - - (3) \\ \\ \bold{Putting \: value \: of \: c \: in \: (2)} \\ :\implies 5c + 4t = 61 \\ \\ :\implies 5 \times \frac{(90 - 5t)}{9} + 4t = 61 \\ \\ :\implies \frac{450 - 25t + 36t}{9} = 61 \\ \\ :\implies 450 + 11t = 549 \\ \\ \end{gathered}

:⟹9c+5t=90−−−−−(1)

:⟹5c+4t=61−−−−−(2)

Usingsubstitutionmethod:

Onsolving(1)weget→

:⟹9c=90−5t

:⟹c=

9

90−5t

−−−−−(3)

Puttingvalueofcin(2)

:⟹5c+4t=61

:⟹5×

9

(90−5t)

+4t=61

:⟹

9

450−25t+36t

=61

:⟹450+11t=549

\begin{gathered}:\implies 11t = 549 - 450 \\ \\ \implies t = \frac{99}{11} \\ \\ \green{:\implies t =9 \: rupees} \\ \\ \bold{Putting \: value \: of \: t \: in \: (3)} \\ :\implies c = \frac{90 - 5 \times 9}{9} \\ \\ :\implies c = \frac{90 - 45}{9} \\ \\ :\implies c = \frac{45}{9} \\ \\ \green{:\implies c = 5} \\ \\ \green{\therefore{\text{ Cost \: of \: 6 \: chairs \: and \: 3 \: tables= 57 \: rupees}}}\end{gathered}

:⟹11t=549−450

⟹t=

11

99

:⟹t=9rupees

Puttingvalueoftin(3)

:⟹c=

9

90−5×9

:⟹c=

9

90−45

:⟹c=

9

45

:⟹c=5

∴ Cost of 6 chairs and 3 tables= 57 rupees