In this section we determine the solutions to a variety of problems by forming and solving suitable linear equations.

Apples cost 55p per kg. Alan buys a bag of apples that costs £1.65. If the bag contains *x* kg of apples,

(a)

write down an equation involving *x*,

It is easier to work in pence.

x × 55 | = | 165 |

55x | = | 165 |

(b)

solve the equation.

x | = | |

x | = | 3 |

Three consecutive whole numbers add up to 36. Determine the three numbers.

If | x = first number, |

then | x + 1 = second number, |

and | x + 2 = third number. |

Adding these gives:

x + (x + 1) + (x + 2) | = | 36 |

3x + 3 | = | 36 |

3x | = | 33 |

x | = | |

x | = | 11 |

and the three numbers are 11, 12 and 13.

A taxi driver charges £2.00 plus £1.10 per mile for all journeys.

(a)

Write down the cost, in pence, for travelling *m* miles.

Basic cost + 110 × number of miles = 200 + 110*m* pence

(b)

The charge for a journey is £3.65. Write down an equation and use this to determine the distance travelled.

200 + 110m | = | 365 |

110m | = | 365 - 200 |

110m | = | 165 |

m | = | |

m | = | 1.5 |

So the distance travelled is 1.5 miles.