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

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

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

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 + 2y        = 300              … (2)