# What is algebra?

• Algebra is used in Maths when we do not know the exact number(s) in a calculation.

• In algebra we use letters to represent unknown values or values that can change.

• Algebra can be used in business when predicting sales, growth and profit.

## Where is algebra used?

Algebra is commonly used in formulas when we do not know at least one of the numbers, or when one of the numbers can change.

### Mathematical formulas

For example, the formula for the area of a rectangle is b × h (b is the base and h is the height.) If the base was 3 cm and the height was 7 cm, then the area would be 21 cm².

A different rectangle could have a base of 4 cm and a height of 10 cm. The area for this would be 40 cm².

As the values for the base and height can be changed, we can use algebra to represent the formula.

### How is algebra used in business?

Algebra can be used to predict sales and how much a customer will spend. Algebra is used to estimate the life time value of a customer, which calculates the percentage of annual spend.

The formula used is:

y = 12 + 8x

Algebra is used because x (the number of months a customer has shopped with us) can change. y represents the percentage that a customer will spend in a year.

Imagine that a customer spends £50 in their first 2 months with us. We have to include their first month as x = 0, so their 2nd month will be x = 1.

Now we know x = 1, we can substitute it into y = 12 + 8x.

Therefore:

y = 12 + (8 × 1)
y = 20%

If 20% = £50. Then over a full year, 100% will equal £250 (5 × £50). This means we can predict a customer will spend £250 a year.