Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved to solve a range of problems in science and engineering.

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In algebra, letters are used to stand for values that can change (**variables**) or for values that are not known (**unknowns**).

A **term** is a number or letter on its own, or numbers and letters multiplied together, such as , or .

An **expression** is a set of terms combined using the operations +, – , x or , for example or .

An **equation** states that two expressions are equal in value, for example .

Pens are sold in packs of 6 and rulers are sold in boxes of 10.

A teacher buys *p* packs of pens and *r* boxes of rulers. Write an expression for the total number of pens and rulers bought.

Firstly, assign letters to the items: for the number of packs of pens and for the number of boxes of rulers.

There are 6 pens in each pack, so the number of pens bought is which is .

There are 10 rulers in each box, so the number of rulers bought is which is .

The number of pens and rulers bought is

A rectangle has a width of cm. The height is 3 cm less than the width. Write an expression for the perimeter of the rectangle.

The perimeter is found by adding together the lengths of the sides of a shape.

The width of the rectangle is given as . The height of the rectangle is 3 less than the width:

Perimeter =

Perimeter =

- Question
John is years old. Kim is three years younger than John. Vanessa is half Kim's age.

Write an expression for each person's age.

From the question, John is years old.

Kim is three years younger than John, so Kim is years old.

Vanessa is half Kim's age, so take Kim's age and divide by 2. This gives Vanessa's age as .