(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

(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

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

X	3	-4	-11
y	5	10	15

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

X	0	2	4
Y	9.2	6.4	3.6

 

Answer

 cost of 1 pencil = Rs 3

Cost of 1 pen = Rs 5