One of the most important things you need to be able to do is work out how you can use algebra to solve a problem that you are given. Students often struggle understanding and interpreting a written problem and rewriting it in terms of algebraic variables. To give you an idea of what to do, we’ll do a few sample problems.

Algebraic translation question Sponsored Links |

John walked a certain distance in the morning, before he had lunch. Then in the afternoon, John walked twice as far as he had in the morning. In total that day John walked 27 km. How far did John walk in the morning? |

Solution |

First things first. We can say with a fair
amount of confidence that the solution to this problem will involve algebra,
as the question is in the algebra section of this book. The general trick
with these questions is to try and So in this question what quantities or amounts are there. Well there’s John, but he’s not really a quantity – he’s just a person. What about lunch – well that’s just a meal, not really an amount or a quantity. What about the distance John walked – bingo! The distance he walked is a quantity – it’s some number of kilometres. Now, in general, you need to So, what we can do is Let x = the distance that John walked in the morning So now we’ve written a simple sentence telling the reader that ‘x’ now represents the distance that John walked in the morning. Another thing that will help you get started in
many algebraic problems is to look for This should make sense – in the afternoon he walked twice as far, so he walked a distance of ‘2x’ in the afternoon, compared with only ‘x’ in the morning. So, we still need to find out how many kilometres
John walked in the morning – in other words we have to find out what ‘x’
equals. We need to write an We already have algebraic expressions for the distance John walked in the morning and afternoon – we can join these together to give the total distance he walked in the day: Now all we have to remember is to write the answer at the end of our solution: Answer: John walked 9 km in the morning. |