# 4 tables and 3 chairs cost Rs.2250 and 3 tables and 4 chairs cost Rs.1950. Find the cost of 1 table and 2 chairs.

Last updated date: 27th Mar 2023

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Answer

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Hint: To solve the question, we have to mathematically represent the given data to calculate the values of the cost of one chair and the cost of one table. The obtained values will lead to the answer of the given question.

Complete step-by-step answer:

Let the cost of one chair and one table be Rs. x, Rs. y respectively.

The given cost of 4 tables and 3 chairs = Rs.2250

When we mathematically represent the above statement we get,

3x + 4y = 2250 …. (1)

The given cost of 3 tables and 4 chairs = Rs.1950

When we mathematically represent the above statement we get,

4x + 3y = 1950 …. (2)

By adding the equation (1) and (2) we get

$\Rightarrow$ 3x + 4x + 3y + 4y = 2250 + 1950

$\Rightarrow$ 7x + 7y = 4200

$\Rightarrow$ 7(x + y) = 4200

$\Rightarrow$ \[x+y=\dfrac{4200}{7}\]

\[\Rightarrow \] x + y = 600 …. (3)

By subtracting the equation (2) from (1) we get

$\Rightarrow$ 3x + 4y – (3y + 4x) = 2250 - 1950

$\Rightarrow$ 4y – 3y + 3x – 4x = 300

$\Rightarrow$ y - x = 300

By adding equation (3) to the above equation, we get

$\Rightarrow$ x + y + y – x = 600 + 300

$\Rightarrow$ 2y = 900

$\Rightarrow$ \[y=\dfrac{900}{2}=450\]

By substituting the above value of y in equation (3), we get

$\Rightarrow$ x + 450 = 600

$\Rightarrow$ x = 600 – 450 = 150

The cost of 1 table and 2 chairs is equal to the value of Rs. (2x + y)

By substituting the x, y values in (2x + y) we get

= \[2\times 150+450\]

= 300 + 450

= Rs. 750

Thus, the cost of 1 table and 2 chairs is equal to the value of Rs. 750.

Note: The possibility of mistake can be not able to represent the given data in a mathematical equation which is helpful in the procedure of solving. The alternative way of solving the question can be using a hit-trial method to calculate the values of the cost of one chair and the cost of one table using the questions framed from the given information.

Complete step-by-step answer:

Let the cost of one chair and one table be Rs. x, Rs. y respectively.

The given cost of 4 tables and 3 chairs = Rs.2250

When we mathematically represent the above statement we get,

3x + 4y = 2250 …. (1)

The given cost of 3 tables and 4 chairs = Rs.1950

When we mathematically represent the above statement we get,

4x + 3y = 1950 …. (2)

By adding the equation (1) and (2) we get

$\Rightarrow$ 3x + 4x + 3y + 4y = 2250 + 1950

$\Rightarrow$ 7x + 7y = 4200

$\Rightarrow$ 7(x + y) = 4200

$\Rightarrow$ \[x+y=\dfrac{4200}{7}\]

\[\Rightarrow \] x + y = 600 …. (3)

By subtracting the equation (2) from (1) we get

$\Rightarrow$ 3x + 4y – (3y + 4x) = 2250 - 1950

$\Rightarrow$ 4y – 3y + 3x – 4x = 300

$\Rightarrow$ y - x = 300

By adding equation (3) to the above equation, we get

$\Rightarrow$ x + y + y – x = 600 + 300

$\Rightarrow$ 2y = 900

$\Rightarrow$ \[y=\dfrac{900}{2}=450\]

By substituting the above value of y in equation (3), we get

$\Rightarrow$ x + 450 = 600

$\Rightarrow$ x = 600 – 450 = 150

The cost of 1 table and 2 chairs is equal to the value of Rs. (2x + y)

By substituting the x, y values in (2x + y) we get

= \[2\times 150+450\]

= 300 + 450

= Rs. 750

Thus, the cost of 1 table and 2 chairs is equal to the value of Rs. 750.

Note: The possibility of mistake can be not able to represent the given data in a mathematical equation which is helpful in the procedure of solving. The alternative way of solving the question can be using a hit-trial method to calculate the values of the cost of one chair and the cost of one table using the questions framed from the given information.

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