Question

2. The cost of two Tables and one Chair is 9000 Rupees and cost of one Table and four Chairs is 8000 Rupees.
a) Form two equations based on the given facts. [2]
b) What is the price of one Chair? What is price of one Table?

Answer 1

Answer:

Let X represent table and Y represent chair

So 1st equation is

2x + y = 9000

And 2nd equation

X + 4y = 8000

Now solving this equations through substitution method we get price price of 1 Table as ₹4000 and price of 1 chair as ₹1000

Answer 2

Given:

The cost of two Tables and one Chair is 9000 Rupees and the cost of one Table and four Chairs is 8000 Rupees.

a) Form two equations based on the given facts.  

b) What is the price of one Chair? What is the price of one Table?

To find:

a) Form two equations based on the given facts.  

b) What is the price of one Chair? What is the price of one Table?

Solution:

(a). Finding the two equations based on the given facts:

Let's say,

"T" → price of 1 table

"C" → price of 1 chair

As per the given facts following are the equations:

The cost of two Tables and one Chair is 9000 Rupees, so we can form the equation as,

$\boxed{\bold{2T + C = 9000}}$ . . . (1)

The cost of one Table and four Chairs is 8000 Rupees, so we can form the equation as,

$\boxed{\bold{T + 4C = 8000}}$ . . . (2)

(b). Finding the price of one chair and one table:

On multiplying equation (2) by 2, we get

2T + 8C = 16000 . . . (3)

On subtracting equations (3) and (2), we get

2T + 8C = 16000

2T + C = 9000

-     -        -

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      7C = 7000

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∴ $\bold{C} = \frac{7000}{7} = \bold{1000}$

On substituting the value of C = 1000 in equation (2), we get

T + (4 × 1000) = 8000

⇒ T + 4000 = 8000

⇒ T = 4000

Thus,

The price of one Chair is → Rs. 1000.

The price of one Table is → Rs. 4000.

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