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Home > Maths I > Relationships > Formulae

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 1 glass square needs 8 metal tubes.

A rhombus shape with all equal length sides. It has short lines dropping vertically from all the corners. The rhombus shape is labelled 'glass square' and the vertical lines are labelled 'metal tubes'

 

A table using 2 glass squares needs 13 metal tubes.

Two rhombuses with equal lengths of sides, adjacent to each other along one edge, like two tables pushed together. The legs of the tables hang down from each corner, sharing legs where the tables are together, making 6 legs.

 

Below is a diagram of a table using 3 glass squares.

Three rhombuses lined up in a line, joined by adjacent sides. Looks like three square tables arranged to make a long table. Table legs hang down from each corner, making 8 legs in total.

 

Now, try these questions.

Question

How many metal tubes are needed for \;3 glass tables?

Answer

\;10 making the frame, plus \;8 legs = \;18 metal tubes

Question

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

Number of glass squares (N)

123456

Number of metal tubes (M)

813
Answer

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, \;M, needed for \;N glass squares.

Answer

M is rising by \;5 each time. The \;5 times table rises by \;5 each time and gives \;5, \;10, \;15, \;20, \;25, \;30. To get the numbers in the table we need to add on {3} each time.

So the formula is:

M = 5N + 3

Question

Each glass square is \;40 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 \;4 metres long for a large office?

Answer

The table is \;400 cm long.

Therefore,

400/40 = 10 is the number of glass squares needed.

i.e. \;{N = 10}

Using the formula M = 5N + 3 with \;{N = 10}, we get

M = 5 \times 10 + 3 = 53

\;53 metal tubes are needed.

 

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