Question

$\huge \fbox \red{❥ Question}$


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.




(REQUIRED QUALITY ANSWER)​

Answer 1

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)

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

Answer 2

x 65 55 45 35

y 20 40 60 80

Let the cost of 1 kg of apples be x and that of 1 kg be y

So the algebraic representation can be as follows:

2x+y=160

4x+2y=300⇒2x+y=150

The situation can be represented graphically by plotting these two equations.

2x+y=160⇒y=160−2x

x 70 60 50 40

y=160−2x 20 40 60 80

2x+y=150⇒y=150−2x

x 65 55 45 35

y=150−2x 20 40 60 80

We can see that the lines do not intersect anywhere, i.e. they are parallel. Hence we can not arrive at a solution.