Understanding Word Problems

Solving word problems requires using mathematical language to describe real-life contexts. Problem-solving strategies are often used in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science). To solve word problems we need to write a set of equations that describes the problem mathematically.

Examples of real-world problem solving applications are:

- modelling population growth;

- modelling effects of air pollution;

- modelling effects of global warming;

- computer games;

- in the sciences, to understand how the natural world works;

- simulators that are used to train people in certain jobs, such as pilots, doctors and soldiers;

- in medicine, to track the progress of a disease.

Problem Solving Strategy
- Read the problem carefully.

- What is the question and what do we need to solve for?

- Assign variables to the unknown quantities, for example, x and y.

- Translate the words into algebraic expressions by rewriting the given information in terms of the variables. - Set up a system of equations.

- Solve for the variables using substitution.

- Check the solution. - Write the final answer. Example 1: Gym membership

Question

The annual gym subscription for a single member is R 1000, while an annual family membership is R 1500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost 5/7 of a family membership. Determine the amount of the proposed increase.

ANSWER

Identify the unknown quantity and assign a variable

Let the amount of the proposed increase be x.

Use the given information to complete a table
__________________________________________
now after increase _________________________________________

single 1000 1000 + x

__________________________________________

family 1500 1500 + x
__________________________________________

Set up an equation

1000+x = 5/7 (1500+x)

Solve for x

7000 + 7x = 7500 + 5x

2x = 500

x = 250

Write the final answer

The proposed increase is R 250.

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