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Maths I

Formulae

# Constructing a formula

## Example

Trendy plc make coffee tables of different sizes.

The smallest has a square glass top sitting on a square metal frame which is supported by four metal legs.

So a table with glass square needs metal tubes.

A table using glass squares needs metal tubes.

Below is a diagram of a table using glass squares.

### Now, try these questions.

Question

How many metal tubes are needed for glass tables?

making the frame, plus legs = metal tubes

Question

Complete the table below to show the number of metal tubes, , needed for different numbers of glass tables, .

Number of glass squares (N)

123456

Number of metal tubes (M)

813

The complete table should be:

Number of glass squares (N)

123456

Number of metal tubes (M)

81318232833
Question

Write down a formula for the number of metal tubes, , needed for glass squares.

M is rising by each time. The times table rises by each time and gives , , , , , . To get the numbers in the table we need to add on each time.

So the formula is:

Question

Each glass square is cm long. Assume that all the metal tubes are the same length (ie. table sides and legs all the same length). How many glass squares and how many metal tubes are needed to make a coffee table metres long for a large office?

The table is cm long.

Therefore,

is the number of glass squares needed.

i.e.

Using the formula with , we get

metal tubes are needed.

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