(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.
Solution:
(i) Let there be x number of girls and y number of boys. As per the given question, the algebraic expression can be represented as follows.
x + y = 10
x – y = 4
Now, for x+y = 10 or y = 10 – x, the solutions are;
| x | 5 | 4 | 6 |
| y | 5 | 6 | 4 |
For x – y = 4 or y = x – 4, the solutions are;
| x | 3 | 4 | 5 |
| y | -1 | 0 | 1 |
The graphical representation is as follows;
From the graph, it can be seen that the given lines cross each other at (7, 3).
Therefore, there are 7 girls and 3 boys in the class.
(ii) Let 1 pencil cost Rs.x and 1 pen cost Rs.y.
According to the question, the algebraic expression can be represented as;
5x + 7y = 50
7x + 5y = 46
For, 5x + 7y = 50 or y = (50 – 5x)/7, the solutions are;
| x | 3 | 10 | -4 |
| y | 5 | 0 | 10 |
For 7x + 5y = 46 or y = (46 – 7x)/5, the solutions are;
| x | 8 | 3 | -2 |
| y | -2 | 5 | 12 |
Hence, the graphical representation is as follows;
From the graph, it can be seen that the given lines cross each other at points (3, 5).
So, the cost of a pencil is Rs. 3/- and the cost of a pen is Rs. 5/-.