1.07 Solving contextual problems with whole numbers

Not all mathematics questions come in the form of an equation. Sometimes we are presented with a real world problem and we want to translate the words into mathematics, so that we can solve the problem

Part of solving word problems comes from understanding the information we are given by reading it carefully, and correctly deciding which mathematical operations to perform. In this lesson we will look at how to turn word problems into a mathematical statement.
 

Worked example

A guitar teacher charges $\$28$$28 for every one hour lesson. How much would it cost for $12$12 lessons?

Think: Let's start by figuring out which steps to perform to solve the problem, then translate those steps into a mathematical statement.

Do: We know that the guitar teacher charges $\$28$$28 for every $1$1 hour. We want to figure out how much it would cost for $12$12 lessons.

If we know every lesson is $1$1 hour, that means we have $12$12 hours' worth of lessons. Every hour is worth $\$28$$28, so we have $28$28 groups of $12$12.

This is the same as $12$12 times $1$1 times $28$28. Translating this into a mathematical sentence gives: $12\times1\times28$12×1×28.

We can now solve to get:

We can now conclude that it would cost $\$336$$336 for twelve lessons.

Reflect: We want to be able to translate the question into mathematical language that makes it easier to follow. We can then identify which operations to use, in order to solve the question. Once that's done, we follow the correct order of operations. In this example the only operation used was multiplication, but in other situations we may need to use a combination of different operations.

Practice questions

question 1

Question 2

Question 3