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## Question 3. 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.

Question 3. 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.

Solution: 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
X         = (160 – ( 0 ))/2         =  80
X         = (160- 80 )/2             = 40
X         = (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
4 x +  2 y        = 300              … (2)
Divide by 2 we get
2 x + y             = 150
Subtract 2x both side we get
Y         = 150 – 2 x
Plug  x = 0 , 50 , 100  we get
Y         = 150 – 2*0                = 150
Y         = 150 – 2* 50             = 50
Y         = 150 – 2 * (100 )      = - 50

 X 0 50 100 Y 150 50 -50

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

Question 3. The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160.