Question

23. Roopesh purchased 3 chairs and one table for Rs 1600 and his friend purchased 5 chairs and 2 tables for
Rs.2900. Ir in both the cases the price of chairs and tables are the same, Roopesh wants to know some
answers of his question what are in his mind. Help him to solve his problem
1) Using the cost price of one chair as 'x and the cost price of one table as'y the linear pair of equations of
the above statements are
a) 3x*y1600 ; 5x+2y-2900
b)3x-y=1600: 5x-2y2900
3xy=1600:5x-2y-2900
d) 3x-y-1600 : 5x+2y-2900
i) The linear pair of equations formed above by the given information are
a) Consistent
b) Inconsistent dependent d) Both (a) and (c)
ii) ir lines are drawn for the linear pair of equations formed by the above information, they will
a) Intersect at one point b) parallel c) coincident d) not exist
iv) The solutions of the linear pair of equations formed by the above information are
a) Rs 300. Rs 700b) Rs.500, Rs 600 c) Rs 450, RS 700 d) Rs. 200, Rs. 1100
v) If Roopesh had purchased 2 chairs and 2 tables the sum of total cost will be
a) Rs 2200 b) Rs 1800
c) Rs 2000
d) Rs 2400

Answer 1

Answer:

I don't know answer sorry

Answer 2

Given:

No. of chairs Roopesh purchased = 3

No. of tables he purchased = 1

Amount for which he purchased both = Rs 1600

No. of chairs Roopesh's friend purchased = 5

No. of tables his friend purchased = 2

Amount for which his friend purchased both = Rs 2900

To find:

Linear pair of equations

To check whether they are consistent, inconsistent or dependent.

To check if the lines intersect, coincide, are parallel to each other or they do exist.

Solutions of the linear pair.

Total cost if Roopesh bought 2 chairs and 2 tables.

Solution:

1) Since, the price of chairs and tables are same in both the cases, let $x$ be the cost price of one chair.

Let $y$ be the cost price of one table.

Then, to find the total price of 3 chairs, multiply the cost of 1 chair with 3 numbers, i.e., $3x$.

The cost of 1 table is $y$ and the total cost of chairs and table is Rs 1600.

Hence, on formulating the above information,

$3x+y=1600$

$3x+y-1600=0$

To find the total cost of 5 chairs his friend bought, multiply the cost of 1 chair with 5 numbers,i.e., $5x$.

To find the total cost of 2 chairs his friend bought, multiply the cost of 1 table with 2 numbers, i.e., $2y$.

The grand total of cost for buying both chairs and tables by Roopesh's friend is Rs 2900.

On formulating,

$5x+2y=2900$

$5x+2y-2900=0$

Thus, the linear pair of equations are:

$3x+y-1600=0\\5x+2y-2900=0$

Hence, option (d) is the correct answer.

i) From the obtained equations,

$3x+y-1600=0\\5x+2y-2900=0$

$a_{1}=3,b_{1}=1,c_{1}=-1600$

$a_{2}=5,b_{2}=2,c_{2}=-2900$

$\frac{a_{1}}{a_{2}}=\frac{3}{5}$

$\frac{b_{1}}{b_{2}}=\frac{1}{2}$

$\frac{c_{1}}{c_{2}}=\frac{-1600}{-2900}= \frac{16}{29}$

Here, $\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}$ .

That means there exist a unique solution to the pair of linear equations. Thus, they are said to be consistent. Hence, the correct answer is option (a).

ii) The graph of these lines are drawn on a graph as plotted below. The lines of these pair of equations intersect at a point A(300,700). Hence, option (a) is correct.

iii) The solution of the linear pair of equations formed above is the point A (300,700) as obtained from the graph. That means, cost of 1 chair is Rs 300 and cost of 1 table is Rs 700. Hence, option (a) Rs 300, Rs 700 is the correct answer.

iv) If Roopesh had purchased 2 chairs and 2 tables, then their total cost will be $2x+2y$. The values of $x$ and $y$ have been determined previously. Substituting those values here:

$2x+2y=2(300)+2(700)=600+1400=2000$ rupees

The total cost of 2 chairs and 2 tables is Rs 2000 and this is given in option (c).

The linear pair of equations are: $3x+y-1600=0$, $5x+2y-2900=0$. Correct answer is option (d).

The linear pair of equations formed are consistent. Correct answer is option (a).

The lines drawn for the linear pair of equations formed above intersect at a point A(300,700). Option (a) is the correct answer.

The solution of the linear pair of equations formed are : Cost of one chair is Rs 300 and cost of 1 table is Rs 700. Option (a) is the correct answer.

If Roopesh had purchased 2 chairs and 2 tables, the sum of total cost will be Rs 2000. Option (c) is the correct answer.