This may seem like a homework problem because it is. However it is not my homework - it belongs to the child I am tutoring, so please feel free to give a full answer, as I will only lead the child along with it and not just fill the answers for him.
The question:
Two stores offer discounts on a particular class of products (let's say laptops). One store offers a discount of 30% off for every hundred dollars you spend. The other offers a 20% discount on your total.
Where should you buy your laptop?
The answer is obviously it depends. Clearly, for prices in even multiples of hundreds, the first offer (30% off every hundred) is far better, but for steps of 100 in \$99 (\$99, \$199, \$299 ....), the second offer is better. And they are equal at steps of 50, as in \$150, \$250, etc.
But how do you represent all this as a mathematical formula? How can you mathematically solve which is better?
I suppose the equations would look something like
$$\frac{7}{10}x + y, \space \space \space \space \space \space \frac{4}{5}(x+y)$$
where $x$ is the multiples of $100$ and $y$ is the number of $1$s. But where do you go from here?
Answer:
Draw out the equation for a price range from 100 to 4000 in increments of 100 and workout the discounted Price, you will find that the 20% discount on the total would be worse than the 30% on every 100 dollars. Chart out the equations in EXCEL and calculate for different prices and compare them. You will find the result self evident as you see below.