9.2 Function machines
Function machines can help when you are working with any formula that has more than one step. The difference between formulas and function machines is that you must follow a function machine in the correct order from left to right, or top to bottom, as shown in the example below. In the Level 2 course on maths you will see that when you use formulas, the BIDMAS rule must be followed.
Example: Car racing
You have been asked to take part in a NASCAR race and have accounted for your fuel and tyres to be able to race for four hours. You find the following method to work out your expected race time:
Your best time for a practice race is 98 minutes. If you race at the same pace, will you complete the race in less than four hours?
Method
Your best practice race is 98 minutes, so you need to put 98 as the first number in the function machine:
98 × 2 + 30 = expected race time
98 × 2 + 30 = 226 minutes
So to answer the question: yes, if you race at the same pace as you race during practice, you would complete the race in under four hours.
Now you have read the example, please have a go at the following activity.
Activity 22: Using function machines
The car sales department decides to hold a marketing event at the office. Following health and safety guidelines it is important to calculate how many people the office will safely hold.
The sales team uses the following rule to work out the number of people that can fit safely in the office.
What is the number of people allowed in the office?
Answer
If you were to write the function machine as a formula, it would look like this:
 (Area of office in square metres × 2) – 10 = number of people allowed in the office
The area of the office in square metres is:
 10 × 20 = 200 m²
So we would replace ‘Area of office in square metres’ in the formula with 200:
 (200 × 2) – 10 = 390
So the maximum number of people allowed in the office is 390 people.

Simon meets a trainer at the leisure centre to set fitness goals. The trainer uses the following rule to calculate Simon’s BMI:
 Simon’s weight in kg ÷ 3 = Simon’s BMI
One of Simon’s fitness goals is to have a BMI between 19 and 25.
He currently weighs 72 kg. Is he meeting his fitness goal?
Answer
Simon’s weight is 72 kg so the calculation is:
 72 ÷ 3 = 24
Simon’s BMI is 24, so he has met his fitness goal.
 Lena makes candles in containers. She knows a rule to work out how much wax she needs (measured in grams) to use for each container (measured in ml):
Lena has a container that holds 200 ml. How many grams of wax should Lena use in this container?
Answer
If you were to write the function machine as a formula, it would look like this:
 (Amount container holds in ml ÷ 10) × 9 = wax needed in g
The container is 200 ml, so we would replace ‘Amount container holds in ml’ in the formula with 200:
 (200 ÷ 10) × 9 = 180
So the maximum amount of wax needed for each container is 180 g.
 Kofi sells souvenir photographs to visitors at the karting centre. The cost price of each photo is £2.
Kofi uses this rule to work out the selling price of each photo that will cover his costs and make a profit:
Kofi thinks that the photos should be sold for £8. Is this correct?
Answer
If you were to write the function machine as a formula, it would look like this:
 (Cost price × 375) ÷ 100 = selling price
The cost price is £2, so we would replace ‘Cost price’ in the formula with 2:
 (2 × 375) ÷ 100 = 7.5
So the selling price should be £7.50, not £8.
You have now completed the section on working with word formulas and function machines. If you did not get the questions correct, please return to them and identify where you went wrong.
Summary
In this section you have learned about working with word formulas and function machines.