## Word Problems on Linear Equations

How to Calculate

Solved Problems :

1. 37 pens and 53 pencils together cost Rs. 320, while 53 pens and 37 pencils together cost Rs. 400. Find the cost of a pen and that of a pencil ?

Solution :

Let the cost of a pen be Rs. x and that of a pencil be Rs. y. Then,

37x + 53y = 320 ...............(i)

and    53x + 37y = 400 ..............(ii)

Adding equations (i) and (ii), we get

90x + 90y = 720 ⇒ x + y = 8 ...........(iii)

Subtracting equation (i) and (ii) , we get

16x - 16y = 80 ⇒ x - y = 5 .............(iv)

Adding equations (iii) and (iv), we get

2x = 13 ⇒ x = 6.5

Substituting x = 6.5 in equation (iii), we get

y = (8 - 6.5) = 1.5

Hence , cost of one pen = Rs. 6.50 and cost of one pencil = Rs. 1.50.

2. A and B each have certain number of apples. A says to B , "If you give me 10 of your apples, I will have twice the number of apples left with you". B replies," if you give me 10 of your apples, i will have the same number of apples as left with you ". Find the number of apples with A and B separately?

Solution:

Suppose A has x apples and B has y apples.

According to the given conditions, we have

x + 10 = 2(y - 10) x - 2y + 30 = 0 ................(i)

and     y + 10 = x - 10     x - y - 20 = 0 ...................(ii)

Subtracting equation (ii) fron equation (i), we get

-y + 50 = 0 y = 50

Substituting y =50 in equation (i) , we get x = 70

Hence A has 70 apples and b has 50 apples.

3. The total expenditure per month of a house hold consist of a fixed rent of the house and mess charges depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3900 for 2 people and Rs. 7500 for 5 people. Find the rent of the house and the mess charges per head per month ?

Solution:

Let the monthly rent of the house be Rs. x and the mes charges per head per month be Rs. y.

According to the given conditions, we have

x + 2y = 3900 ..........(i)

x + 5y = 7500 ..........(ii)

Subtracting equation (ii) from equation (i), we get

- 3y = -3600 ⇒ y = 1200

Putting y = 1200 in equation (i), we get x = 1500

Hence , monthly rent = Rs. 1500 and mess charges per head per month = Rs. 1200