**Question 1 (ii). 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen**

Solution: Let cost of pencil = Rs x

Cost of pens = Rs y

5 pencils and 7 pens together cost Rs 50,

So we get

5x + 7y = 50

Subtract 7y both side we get

5x = 50 – 7 y

Divide by 5 we get

X = 10 - 7 y /5

Plug value of y which is factor of 5 to get whole number so plug y = 5 , 10 and 15 we get

X = 10 – 7 * 5 / 5 = 10 – 7 = 3

X = 10 – 7 * 10 / 5 = 10 – 14 = - 4

X = 10 – 7 * 15 / 5 = 10 – 21 = - 11

Given that 7 pencils and 5 pens together cost Rs 46

7 x + 5 y = 46

Subtract 7x both side we get

5y = 46 – 7x

Divide by 5 we get

Y = 46 / 5 - 7 x / 5

Y = 9.2 – 1.4 x

Plug x = 0 , 2 and 4 we get

Y = 9.2 – 1.4 * 0 = 9.2 – 0 = 9.2

Y = 9.2 – 1.4 (2) = 9.2 – 2.8 =6.4

Y = 9.2 – 1.4 (4) = 9.2 – 5.6 = 3.6

**Answer ** ** cost of 1 pencil = Rs 3** **Cost of 1 pen = Rs 5 **