Sunday, March 31, 2013

(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
        = 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
        = 46 / 5   - 7 x / 5
        = 9.2 – 1.4  x
Plug x  = 0 , 2 and 4 we get
        =  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

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