Worded percentage problems

These are just some simple questions that I ended up writing because I couldn’t find any that contained a suitable mixture.  I wanted worded problems that combined % increase, % decrease and % of an amount, but didn’t delve into reverse percentage.  Enjoy, use, adapt…

Warehouse

No 1 in a series of posts based on Thinking Mathematically (1985) by Mason, Burton, Stacey

This question prompts learners to come up with their own specific example(s) of a price to apply the discount and sales tax to.  It made me think that there are many questions I use in class which I could adapt (i.e. remove the specific example) to get my students better acquainted with this step.

I used £100 and performed the calculation mentally. It prompted me to reflect on how I chose £100 and how I would help my students make good choices for examples.

I think a number of my students might think that they have seen something a bit like this before:

```"A price is reduced by 20% in a sale but this price is then reduced by a further 10% by using a voucher code"

Amy says that the overall reduction is 30%. Explain why she is wrong.```

Depending on the class, I might use these two examples together to highlight the process of moving through from the specific by choosing good examples to the general using basic algebraic notation with decimal multipliers.

In the first example, we need to get to:

`0.8 x 1.15 x P = 1.15 x 0.8 x P`

In the second case:

`0.8 x 0.9 x P ≠ 0.7 x P`

These statements alone are insufficient “explanations” in the context of the question, so there could be a good opportunity here to work on some specific exam technique as these types of questions often pose difficulty for students.