The cost of 2 kg of apples and 1 kg 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.
Solution 1
Let the cost of 1 kg of apples be Rs x.
And, cost of 1 kg of grapes = Rs y
According to the question, the algebraic representation is
2x + y = 160
4x + 2y = 300
For 2x + y = 160
y = 160 - 2x
The solution table is
x |
50 |
60 |
70 |
y |
60 |
40 |
20 |
For 4x + 2y = 300,
`y = (300 - 4x)/2`
The solution table is
x |
70 |
80 |
75 |
y |
10 |
−10 |
0 |
The graphical representation is as follows
Solution 2
Cost per kg of apple = Rs x
Cost per kg of grapes = Rs y
Algerbraically 2x + y = 160 ...........(1)
4x + 2y = 300 or 2x + y = 150 ..........(2)
From (1) y = 160 - 2x
x | 50 | 60 |
Y = 160 - 2x | 60 | 40 |
From (2), y = 150 - 2x
x | 50 | 60 |
Y = 150 - 2x | 50 | 30 |
The graphical representation is as follow