Solving Word Problems Revision Notes for Leaving Cert Mathematics

Solving Word Problems

Word problems in algebra can be challenging because they require translating real-world scenarios into mathematical equations. The key is to break the problem into manageable steps and systematically solve it.

Read Carefully: Read the problem thoroughly to understand what is being asked.
Identify the Goal: Determine what the problem is asking you to find (e.g., a number, a distance, a time, etc.).
Highlight Key Information: Mark important details such as quantities, relationships, and constraints.
Choose Variables: Assign variables to the unknowns. For example:
- Use $x, y$ , etc., for numbers.
- Use $t$ for time, $d$ for distance, etc., when appropriate.

Example

infoNote

The difference between half a number and one-third of the same number is 69. What is the number ?

First identify the key word :

The difference between half a number and one-third of the same number is 69. What is the number ?

Replace the objects in the question (numbers) with appropriate variable names.

The difference between half of $x$ and one-third of $x$ is 69. What is the number ?

Half of $x$ : $\tfrac{x}{2}$ .

One-third of $x$ : $\tfrac{x}{3}$ .

Difference between half of $x$ and one-third of $x$ : $\tfrac{x}{2}-\tfrac{x}{3}$

Equation :

\frac{x}{2}-\frac{x}{3}=69

Equation :

\frac{6x}{2}-\frac{6x}{3}=414

3x-2x=414

x=414

Solving Word Problems (Leaving Cert Mathematics): Revision Notes