Sometimes making slight changes to the scenario can make a difference, and sometimes it does not.
Changes can be made to the following parameters:
Quantities
Example: When you go shopping at Publix you can buy a single bottle of water for $1 or a six-pack of identical bottles for $4 for a cheaper unit price. However, when you fill up for gas it is the same unit price whether you buy 1 gallon or 16 gallons of gas.
The time scale (longer or shorter)
Ratios, for example if you drive twice as long at a constant speed. Be careful because realistically you might have to stop to buy more fuel, bathroom breaks, eat, etc.
Prices (discounts/markups)
Example: individuals can buy a small pack of markers, but schools can buy much larger quantities at a discount.
Tariffs (taxes)
Example: New tariffs on imported goods from a country result in higher prices and possibly less people buying them
The law
Examples: (1)Laws that require seat belts have saved an estimated 15,000 lives in the US in 2007. (2) Laws that require bike helmets result in fewer people riding bikes.
As well as others
Example: extending graphs drawn from data you have collected. If you have a years worth of data showing a positive correlation and average increase of 50 sales per month you can make predictions about the following year from the pattern.
Let’s take a look at the example activity from the Cambridge International AS & A Level Thinking Skills Coursebook.
Example Activity 12.1:
Abigail runs 100 m in 11 seconds, whereas Ella runs 200 m in 23 seconds. They maintain these speeds for a race of 1 km. Who wins and by how many seconds?
What is the problem with the scenario in this question? Are the numbers in the question realistic?
Commentary:
We could easily answer the question. 1km is 10 x 100m, so at a constant speed it would take Abigail 10 x 11 seconds to run 1 km. This is 110 seconds, or 1 minute and 50 seconds.
1 km is 5 x 200m, so at a constant speed it would take Ella 5 x 23 seconds to run 1 km. This is 115 seconds, or 1 minute and 55 seconds. Abigail therefore wins by 5 seconds.
The problem here is that it isn’t realistic for the runners to maintain their speeds over longer distances. Running 100 m in 11 seconds is fast! Maintaining this over a longer distance would be impossible. In fact, the fastest women’s 800 m ever (as of 2017) was completed in 1 minute and 53 seconds. It is clearly impossible for Abigail to run 1,000 m in a shorter time than this.