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Solving Algebra Problems - Example

We shall test our method of thinking on solving the following algebra problem.

Example :

At a stall that pays a $4 rent per day, the stall keeper is selling 4 oranges and 1 lemon for $1.9. He also sells 2 lemons and 2 oranges for $1.4. Assuming that the prices of the fruits are fixed, what is the price of a lemon?

What are we trying to find?

We realize that we are trying to find the price of a lemon and not of an orange.

What information do we need?

We need the information that states ‘selling 4 oranges and 1 lemon for $1.9' and ‘sells 2 lemons and 2 oranges for $1.4'. The rent of the stall does not matter in the question. It was placed there to trick students.

How are we going to approach this algebra problem?

It would not be a good idea to use the 'trial and error' method as it will take ages to guess the answer correctly.Besides, there is a more suitable method to approaching this algebra problem.

After careful consideration, we decide to use simultaneous equations.

Like all problems, we have to define the variables. Here, we define the price of an orange to be x and the price of a lemon to be y.

Knowing that the price of a lemon (y) is our main priority, we use the elimination method and construct the two following equations based on the algebra problem.

4x + y = 1.9 (1st)

2x + 2y = 1.4 (2nd)

We multiply the 2 nd equation by two and minus it with the first equation, leaving y as the only variable.

4x + 4y – (4x + y) = 2.8 – 1.9

Then we simply divide to obtain the price of lemon.

3y = 0.9

y = $0.3

Then we conclude with a sentence like ‘The price of a lemon is $0.3.' for neat presentation.

Try solving other algebra problems using this process of thinking that you have just learnt.

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