(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/-.