1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.
2. The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
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 Rs300. . Represent this situation algebraically and geometrically.
Solution 1:
Let age of Aftab is represented by x
And age of daughter is represented by y
Then Seven years ago,
Age of Aftab = x 7
Age of daughter = y7
As per the question Aftab was seven times as old as her daughter then were so we get
(x – 7) = 7 (y – 7)
x – 7y = 42 …(1)
Now Three years from now ,
Age of Aftab = x +3
Age of daughter = y+3
As per question Aftab shall be three times as old as her daughter will be so we get
x + 3 = 3 (y + 3)
x 3 y = 6 …(2)
Algebraic representation of situation
x – 7 y =  42 …(1)
x 3 y = 6 …(2)
To represent it graphically, we need to plot these equation on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
x – 7 y =  42
or
y=(x+42)/7
X 
0 
7 
Y=(x+42)/7 
6 
7 
x 3 y = 6
y=(x6)/3
X 
0 
6 
Y=(x6)/3 
2 
0 
We can plot these two lines on XY coordinate system using the two point derived above
Solution 2:
Let Cost of one bat = Rs x
Let Cost of one ball = Rs y
3 bats and 6 balls for Rs 3900 So that
3 x + 6y = 3900 … (1)
Given that she buys another bat and 2 more balls of the same kind for Rs 1300
So we get
x + 2 y = 1300 … (2)
Algebraic representation of situation
3 x + 6y = 3900 … (1)
x + 2 y = 1300 … (2)
To represent it graphically, we need to plot these equation on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
3x +6y = 3900
or
y=(39003x)/6
X 
1300 
1300 
y=(39003x)/6

1300 
0 
x +2 y = 1300
y=(1300x)/2
X 
1300 
1300 
y=(1300x)/2 
0 
1300 
Solution 3:
Let cost each kg of apples = Rs x
Cost of each kg of grapes = Rs y
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)
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300
so we get
4x + 2y= 300 … (2)
Algebraic representation of situation
2 x + y = 160 … (1)
4x + 2y= 300 … (2)
To represent it graphically, we need to plot these equation on the XY coordinate system.
We can choose two values of each equation and plot it on XY coordinate system
2x +y = 160
or
y=1602x
X 
80 
40 
y=1602x

0 
80 
4x + 2y= 300
y=(3004x)/2
X 
0 
50 
y=(3004x)/2 
150 
50 