Question

The cost of 2kg of apples and 1kg pf grapes on a day was found to be rs 160. After moth the cost of 4kg of apples and 2kg of grapes is rs 300 represent the situation algebraically and geometrically

Answer 1

Answer:-

Let the cost of Apples per kg be Rs x

Let the Cost of Grapes per kg be Rs y

Given That:-

2 kg apples and 1 kg grapes cost Rs 160

⇒2 × Cost per kg of Apples + 1 × Cost per kg of grapes = 160

⇒2 + y = 160 ____ (1)

Also:-

4 kg apples and Grapes cost Rs 300

⇒4 × Cost per kg of Apples + 2 × Cost per kg of grapes = 300

⇒4x + 2y = 300

⇒2 (2x + y) = 2 × 150

⇒2x + y = 150 ____ (2)

Now:-

Plotting Equations

➫2x + y = 160 ____ (1)

➫2x + y = 150 ____ (2)

For Equation (1):-

⇨2x + y = 150

Let x = 50

➨20 (50) + y = 150

➨100 + y = 150

➨y = 150 - 100

➨y = 50

So:-

⇨x = 50, y = 60 is a solution

I.e, (50, 60) is a solution..

Let x = 60

➨2 (60) + y = 150

➨120 + y = 150

➨y = 150 - 120

➨y = 30

So:-

⇨x = 60, y = 30 is a solution

I.e, (60, 30) is a solution..

For Equation (2):-

➫2x + y = 160

Let x = 50

➨2 (50) + y = 160

➨100 + y = 160

➨y = 160 - 100

➨y = 60

So:-

⇨x = 50, y = 60 is a solution

I.e, (50, 60) is a solution..

Let x = 60

➨2 (60) + y = 160

➨120 + y = 160

➨y = 160 - 120

➨y = 40

So:-

⇨x = 60, y = 40 is a solution

I.e, (60, 40) is a solution..

➼Refer the attachment for graph :)