Question

The price of 4 chairs and 8 tables is 4800Rs and price of 8 chairs and 4 tables is 6500 Rs then find price of 2 chairs and 2 tables.​

Answer 1

Answer:

Step-by-step explanation:

Let the price of 1 chair be, x

and the price of 1 table be, y

Now, Given that

i) The price of 4 chairs and 8 tables is 4800 rupees, and

ii)  The price of 8 chairs and 4 tables is 6500 rupees

Let's form equations of the above,

i) 4x + 8y = 4800 ⇒ equation 1

ii) 8x + 4y = 6500 ⇒ equation 2

Let's solve the above 2 equations,

Dividing equation 1 by 4, we get ,

x + 2y = 1200 ⇒ equation 1

Dividing equation 2 by 2, we get ,

4x + 2y = 3250 ⇒ equation 2

Subtracting equation 1 from equation 2,

(4x + 2y) - (x + 2y) = 3250 - 1200

Solving the brackets,

4x + 2y - x - 2y = 2050 ( - multiplied by + gives -)

Simplifying the above equation,

3x = 2050

∴ x = $\frac{2050}{3}$

This is the price of 1 chair.

The price of 2 chairs = 2x = 2 x $\frac{1550}{3}$ = 1033.333

Inserting the value of x in equation 1 to find value of y,

$\frac{2050}{3}$ + 2y = 1200

∴ 2y = 1200 -  $\frac{2050}{3}$

∴ 2y =  $\frac{3600 - 2050}{3}$

∴ 2y =  $\frac{1550}{3}$

Therefore, the price of 2 tables is $\frac{1550}{3}$, i.e, 516.667