Question

Form the pair of linear equations in the following: 10 erasers and 14 sharpeners together cost Rs 100, whereas 35 erasers and 25 sharpeners together cost Rs 230. Find the cost of one eraser and that of one sharpener using graphical method and choose the solution below.

Answer 1

In the above Question , the following information is given -

We have to sets of conditions given from which we need to form linear equations -

Condition 1 -

10 erasers and 14 sharpeners together cost Rs 100 .

Condition 2 -

35 erasers and 25 sharpeners together cost Rs 230

Converting into linear equations -

Let us assume that erasers are depicted by x and sharpeners are depicted by y .

Here ,

10 erasers and 14 sharpeners together cost Rs 100 .

So , equation 1 becomes -

Equation 1 -

10x + 14y = 100

35 erasers and 25 sharpeners together cost Rs 230

So , equation 2 becomes -

Equation 2 -

35x + 25y = 230 .

Equation 1 can be further simplified to get -

5x + 7y = 50 .......... { 1 }

Equation 2 can be further simplified to get -

7x + 5y = 46 ......... { 2 }

So , we can finally obtain the following equations -

5x + 7y = 50 .......... { 1 }

7x + 5y = 46 ......... { 2 }

Solution By Graphical Method -

Draw the graphs for each of the corresponding equations -

Equation 1 -

5x + 7y = 50 .......... { 1 }

Corresponding Graph -

See the first attachment .

Equation 2 -

7x + 5y = 46 ......... { 2 }

Corresponding Graph -

See the second attachment .

The solutions are the only pair of values of x and y for which the two lines intersect .

There is only 1 such Solution .

To view that , see the third attachment .


The only solution is when x = 3 and y = 5 .

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