The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically
Solution:
(i) The cost of 2 kg of apples and 1 kg of grapes is ₹ 160
(ii) The cost of 4 kg of apples and 2 kg of grapes is ₹ 300
Let, the cost of 1 kg apples = ₹ x
The cost of 1 kg grapes = ₹ y
The two linear equations can be formed for the above situation.
Cost kg 2 kg apples and 1 kg of grapes are ₹ 160. Mathematically it can be represented as,
2x + y = 160 --- Equation(1)
Also, cost of 4 kg apples and 2 kg of grapes are ₹ 300. Mathematicallyit can be represented as,
4x + 2y = 300
2(2x + y) = 300
2x + y = 150 --- Equation(2)
Therefore, the algebraic representation for equation(1) is:
2x + y = 160
y = 160 - 2x
And, the algebraic representation for equation(2) is:
2x + y = 150
y = 150 - 2x
For the representation of these equations graphically, we need at least two solutions for each equation. Let's tabulate the solutions as shown below.
The graphical representation is as follows:
x-axis: 1 unit = ₹10, y-axis: 1 unit = ₹10
Since the lines are parallel, hence there is no solution.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 3
Video Solution:
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically
NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.1 Question 3
Summary:
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. The situation is represented algebraically and geometrically. On representing the solution graphically the lines are found to be parallel and hence, no solution
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