In this section we make use of formulae and develop simple formulae ourselves. First we begin with some revision of working with *negative numbers*.

If *a* = 6, *b* = –5, *c* = –7 and *d* = 3, calculate:

(a)

a + c

a + c | = 6 + (-7) |

= 6 - 7 | |

= -1 |

(b)

a - b

a - b | = 6 - (-5) |

= 6 + 5 | |

= 11 |

(c)

bc

bc | = (-5) × (-7) |

= 35 |

(d)

b^2 + cd

b^2 + cd | = (-5)^2 + (-7) × 3 |

= 25 + (-21) | |

= 25 - 21 | |

= 4 |

A triangle has sides of length *x*, *x* + 4 and *x* + 8, as shown in the diagram.

(a)

Write down a formula for the perimeter, *p*, of the triangle.

p | = x + (x + 4) + (x + 8) |

p | = 3x + 12 |

(b)

Calculate the perimeter when *x* = 10.

p | = 3 × 10 + 12 |

p | = 30 + 12 |

p | = 42 |

(c)

Calculate *x* when the perimeter is 45.

45 | = 3x + 12 | |

33 | = 3x | Subtracting 12 from both sides |

x | = | Dividing both sides by 3 |

x | = 11 |

A removal firm charges £80 plus £2 for every mile that their removal van travels.

(a)

Write down a formula for the cost, £*C*, of a move of *n* miles.

*C* = 80 + 2*n*

(b)

Calculate the cost of moving 262 miles.

C | = 80 + 262 × 2 |

C | = 80 + 524 |

C | = £604 |

(c)

A move costs £500. How far did the removal van travel?

500 | = 80 + 2n | |

420 | = 2n | Subtracting 80 from both sides |

n | = | Dividing both sides by 2 |

n | = 210 miles, so the van travelled 210 miles. |

Note: To type indeces on this page use ^ sign. e.g. *n*^{2}: