Question

Case Study II: linear equations Rahul and Sarita went to market to purchase a pen. Cost of pen was Rs10. They both contributed Rs x and y respectively to buy the pen. This situation forms a linear equation x + y = 10. From the below graph of linear equation x + y = 10, (i) Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes. (ii) Find the contribution of Rahul if Sarita's share was Rs7. *
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Answer 1

SOLUTION

GIVEN

• Rahul and Sarita went to market to purchase a pen

• Cost of pen was Rs 10

• They both contributed Rs x and y respectively to buy the pen

• This situation forms a linear equation x + y = 10

TO DETERMINE

From the graph of linear equation x + y = 10

(i) Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes

(ii) Find the contribution of Rahul if Sarita's share was Rs 7

EVALUATION

Here it is given that Rahul and Sarita went to market to purchase a pen

They both contributed Rs x and y respectively to buy the pen

So their total contribution = Rs ( x + y )

Now Cost of the pen was Rs 10

Hence This situation forms a linear equation

$\sf{x + y = 10 \: \: \: .......(1)}$

We draw this linear equation in graph in Cartesian Coordinate system

Graph : For graph refer to the attachment

Now the line x + y = 10 cuts X axis at A( 10, 0) & Y axis at B( 0, 10)

(i) Now OAB is the area bounded by the line x + y = 10 and both the co-ordinate axes

The triangle OAB is right angle triangle

So the area of the triangle

$\displaystyle \sf{ = \frac{1}{2} \times 10 \times 10} \: \: \: sq \: unit$

$\displaystyle \sf{ = 50} \: \: sq \: unit$

(ii) Now Sarita's share was Rs 7

So y = 7

Hence from the equation (1) we get

$\sf{x + 7 = 10}$

$\implies \: \sf{x = 3}$

Hence the contribution of Rahul is Rs 3

From graph it can also be verified

Sarita's share was Rs 7

So y = 7

Let C denote the point ( 0, 7 )

Now the line parallel to X axis passing through the point C ( 0, 7 ) intersects line given by Equation (1) at D( 3, 7 )

So the abscissa of D is 3

Hence the contribution of Rahul is Rs 3

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