Question

Binu bought 5 rulers, 7 ink pads and 3 pens at a cost of Rs.52. Rosy bought 4 pens , 6 ink pads and 7 rulers for Rs.53 when Paul bought 7 pens and 3 ink pads, the shop keeper took a 50rupees. Find the cost of each.​

Answer 1

Given :

Cost of 5 rulers, 7 ink pads and 3 pens = Rs 52

Cost of 4 pens , 6 ink pads and 7 rulers = Rs 53

Cost of 7 pens and 3 ink pads = Rs 50

To find:

The cost of each ruler, ink pad and pen.

Solution :

Let as assume,

Rate of ruler = x

Rate of ink pad = y

Rate of pen = z

It is given that,

Cost of 5 rulers, 7 ink pads and 3 pens = Rs 52

Cost of 4 pens , 6 ink pads and 7 rulers = Rs 53

Cost of 7 pens and 3 ink pads = Rs 50

So,

these all conditions says that :

$5x + 7y + 3z = 52 \: \: \: \: \: \: \: (1) \\ 7x + 6y + 4z = 53 \: \: \: \: \: \: \: (2) \\ 3y + 7z = 50 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (3)$

(equation 1, 2 and 3 respectively)

We will first eliminate at least one unknown, so that we can find the values of two other un knowns,

So, for eliminating x,

On multiplying equation 1 by 7, we get :

$35x + 49y + 21z = 364$

(equation 4)

and multiplying equation 2 by 5, we get :

$35x + 30y + 20z = 265$

(equation 5)

On subtracting equation 4 by 5 , we eliminate x and get :

$19y + z = 99$

(equation 6)

On multiplying equation 6 by 7, we get :

$133y + 7z = 693$

(equation 7)

on subtracting equation 7 by equation 3, we eliminate z and get :

$130y = 643$

so,

$y = \frac{643}{130} = 4.95$

On putting value of y in equation 6, we get

$(19\times \frac{643}{130}) + z = 99$

on solving,

z = 4.95

On putting value of y and z in equation 1, we get

$5x + (7 \times 4.95) + (3 \times \: 4.95) = 52$

on solving,

x = 0.5

So,

Rate of ruler = x = Rs 0.5

Rate of ink pad = y = Rs 4.95

Rate of pen = z = Rs 4.95

Answer 2

Given:

Binu bought 5 rulers, 7 ink pads and 3 pens at a cost of Rs. 52.

Rosy bought 4 pens , 6 ink pads and 7 rulers for Rs. 53

Paul bought 7 pens and 3 ink pads for Rs 50.

To find:

Find the cost of each.​

Solution:

Let "x" represent the ruler

"y" represent the ink pad

"z" represent the pens

5x + 7y + 3z = 52  ..........(1)

7x + 6y + 4z = 53 .......(2)

3y + 7z = 50 ..........(3)

7 × (1) - 5 × (2) gives

19y + z = 99 .........(4)

solving (3) and (4) we get,

y = 643/130 = 4.94

z = 653/130 = 5.02

substituting the above values in (1), we get,

5x + 7y + 3z = 52

5x + 7 (4.94) + 3 (5.02) = 52

5x + 34.51 + 15.06 = 52

5x = 2.43

x = 0.486

Therefore, the cost of ruler = x = Rs. 0.486

the cost of ink pad = y = Rs.  4.94

the cost of pen = z = Rs. 5.02