Ex 3.1, 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.
Let the Cost of Apples per kg be Rs x
& let 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
2x + y = 160
Also,
4 kg apples and 2 kg 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
Now, plotting equations
2x + y = 160 ...(1)
2x + y = 150 …(2)
For Equation (1)
2x + y = 150
Let x = 50
2(50) + y = 150
100 + y = 150
y = 150 − 100
y = 50
So, x = 50, y = 50 is a solution
i.e. (50, 50) 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
We will plot both equations on the graph

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.