Sunday, March 31, 2013

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Let cost each kg of apples  = Rs x
Cost of each kg of grapes  = Rs  y
 Given that The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160
So that
2 x +  y  = 160              … (1)
2x          = 160  - y
x            =  (160 – y)/2
Let y = 0 , 80  and 160  we get
= (160 – ( 0 ))/2   =  80
= (160- 80 )/2      = 40
= (160 – 2* 80 )/2 = 0
X
80
40
0
y
0
80
160

Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300
so we get
4x +  2y= 300              … (2)
Divide by 2 we get
2x + y   = 150
Subtract 2x both side we get
y         = 150 – 2 x
Plug  x = 0 , 50 , 100  we get
        = 150 – 2*0                = 150
        = 150 – 2* 50             =  50
        = 150 – 2 * (100 )      = - 50
X
0
50
100
Y
150
50
-50

Algebraic representation
2 x + y          = 160              … (1)
4 x + 2y        = 300              … (2)

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