Linear equations can really help Year 8 students when they shop. They make it easier to understand budgeting and prices. Here are some simple examples:

1. Budgeting: Imagine a student has £50 to spend on school supplies. They can use an equation to keep track of their money. Let’s say notebooks cost £3 each and pens cost £1 each. They can write this as:

   $$3n + p \leq 50$$

   Here, $n$ is the number of notebooks, and $p$ is the number of pens. This way, they know they can't spend more than £50.

2. Discounts: Sales are fun because of discounts! If something costs £100 and has a 20% discount, students can calculate how much it costs after the discount. They can use:

   $$P = 100 - 0.2(100)$$

   This means the sale price is £80, which helps them see if they can afford it.

3. Comparing Prices: When students want to buy two different products, they can set up equations to see which one is cheaper. If Product A costs £x and Product B costs £y, they can compare with:

   $$x < y$$

   This tells them which product they should buy.

These examples not only help with math skills but also teach students about managing money better.