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

let chairs be X

and tables be Y

so,

According to first case

9x +5Y=90

According to second case

5X+4Y=61

from first and second cases we can find price of each chair and table

9X+5Y=90

5X+4Y=61

by elimination method

5(9x+5y=90)

9(5x+4y=61)

45x+25y=450

45x+36y=549

by subtracting two equations u get

-11y=-99

Y=9 by substituting in any one equation we can find X

9X+5×9=90

9X+45=90

9X=45

X=5

therefore we found price of chairs and table

cost of 6chairs and 3 tables is

6×5=35

3×9=27

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\bold{\therefore Cost\:of\:6\:chairs\:and\:5\:tables=57\:rupees}}$

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

• 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.

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

• According to given question :

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

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