Calculating Change: A Practical Maths Problem

Understanding how to calculate change is a fundamental skill, useful in everyday life. Let’s break down a common scenario and solve it step-by-step.

The Problem:

Rizwan makes the following purchases:

• 6 stamps at 25p each
• 2 packs of postcards at 89p per pack
• 1 pack of labels at £1.09

He pays with a £10 note. How much change should Rizwan receive?

Solution:

Here’s how to solve this problem:

Calculate the cost of the stamps:

• Cost per stamp: 25p
• Number of stamps: 6
• Total cost of stamps: 25 \text{p} \times 6 = 150 \text{p}

Calculate the cost of the postcards:

• Cost per pack: 89p
• Number of packs: 2
• Total cost of postcards: 89 \text{p} \times 2 = 178 \text{p}

Convert the cost of the labels to pence:

• Cost of labels: £1.09
• Conversion: £1 = 100p
• Total cost of labels: 1.09 \times 100 = 109 \text{p}

Calculate the total cost of all items in pence:

• Total cost = Cost of stamps + Cost of postcards + Cost of labels
• Total cost = 150 \text{p} + 178 \text{p} + 109 \text{p} = 437 \text{p}

1. Convert the amount paid to pence:
   • Amount paid: £10
   • Conversion: £1 = 100p
   • Amount paid in pence:  10 \times 100 = 1000 \text{p}

Calculate the change:

• Change = Amount paid – Total cost
• Change = 1000 \text{p} - 437 \text{p} = 563 \text{p}

1. Convert the change back to pounds and pence:
   • Change in pence: 563p
   • £4 = 400p
   • Therefore, change = £5.63

Answer: Rizwan should receive £5.63 in change.

Why This Matters

This type of problem reinforces several important mathematical skills:

• Multiplication: Calculating the total cost of multiple items.
• Addition: Summing the costs of different items.
• Unit Conversion: Converting between pounds and pence.
• Subtraction: Calculating the difference between the amount paid and the total cost.

These skills are not only essential for exams but also for managing your finances in the real world. For more help with similar problems, consider consulting a UK GCSE Maths Tutor.