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Question:
Form the pair of linear equations in the following problems, and find their solutions graphically.
(i) 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
Answer:
Solutions:
(i) 10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
Let the number of boys who took part in the quiz is x and the number of girls who took part in the quiz is y.
According to given conditions, we have
x + y = 10 … (1)
And, y = x + 4
⇒ x - y = - 4 … (2)
For equation x + y = 10, we have the following points which lie on the line.
x |
0 |
10 |
y |
10 |
0 |
For equation x – y = –4, we have the following points which lie on the line.
x |
0 |
-4 |
y |
4 |
0 |
We plot the points for both of the equations to find the solution.
We can see that the intersection point of two lines is (3, 7).
Therefore, the number of boys who took part in the quiz is 3 and, the number of girls who took part in the quiz is 7.
(ii) 5 pencils and 7 pens together cost Rs 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
Let the cost of one pencil is Rs and Let the cost of one pen is Rs
According to given conditions, we have
For equation we have the following points which lie on the line.
x |
10 |
3 |
y |
0 |
5 |
For equation we have the following points which lie on the line.
x |
8 |
3 |
y |
-2 |
5 |
We plot the points for both of the equations to find the solution.
We can see that the intersection point of two lines is (3, 5).
Therefore, the cost of a pencil is Rs 3 and, the cost of a pen is Rs 5.
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