Constructing formulae

Introduction to formulas poster

The advert says that the cost of a party is \pounds{50} plus \pounds{5} per person, so what would be the cost of a party for {10}?

The cost would be \pounds{50}+(\pounds{5}\times{10})=\pounds{50}+\pounds{50}=\pounds{100}.

Question

What would be the cost of a party for {20}?

\pounds{50}+(\pounds{5}\times{20})=\pounds{50}+\pounds{100}=\pounds{150}

How do you work out the cost if you don't know the number of people who will attend the party?

Call the number of people ' {n}'.

The cost for {10} people is \pounds{50}+(\pounds{5}\times{10})=\pounds{100}.

The cost for {20} people is \pounds{50}+(\pounds{5}\times{20})=\pounds{150}.

So the cost for {n} people is \pounds{50}+(\pounds{5}\times{n})=\pounds({50}+{5n}).

With this formula you can work out the cost of a party for any number of people.

Have a go at the next question to see if you can use {n} in another expression.

Question

Alexa is {12} years old. How old will she be in {n} years' time?

In {n} years' time her age will have increased by {n}. So her age will be {n} more than it is now.

Her age will be:

12 + n

Check your answer. In one year's time she will be {13}. If we put {1} in for the value of {n} we get 12 + 1 = 13. So that is correct.

In ten years' time she will be {22}, and putting n=10 gives us:

age = 12 + 10 = 22

So the formula is correct.