Substitution

Substitution is the process of replacing the words or letters in an equation with numbers.

You will need to be familiar with the order of operations BIDMAS.

Cost of hiring a van = number of days × £40 + £100

If the van is hired for 3 days, how much will this cost?

1. Replace the number of days with 3:

Cost = 3 × £40 + £100.

2. Don’t forget BIDMAS, you must multiply first and then add.

Cost = £120 + £100.

Cost = £220.

Question

Cost of hiring a van = number of days × £40 + £100.

Calculate the cost if the van is hired for 6 days.

This plumber’s wages are calculated using the formula:

Wages = number of hours × £15 + £45.

If he earns £105, how many hours did he work for?

1. Replace wages with £105:

£105 = number of hours × £15 + £45.

2. You need to get ‘number of hours’ on its own. You may want to revise solving equations.

Start by subtracting £45 from both sides:

£105 - £45 = number of hours × £15.

£60 = number of hours × £15.

3. Then divide both sides by £15:

£60 ÷ £15 = number of hours.

Number of hours = 4.

Wages = number of hours × £15 + £45.

Calculate the number of hours worked if the wages are £150.