Question

.. The area of a garden plot can be represented
by the expression 84z - 54. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.

Answer 1

The area of each section is 14z - 9

Solution:

The area of a garden plot can be represented  by the expression 84z - 54

The garden will be  divided into six sections for planting six different  vegetables

The sections will be equal in area.

To find: Expression for area of each section

Number of sections = 6

$Area\ of\ each\ section = \frac{\text{Total area of graden}}{\text{Number of sections}}$

$Area\ of\ each\ section = \frac{84z-54}{6}\\\\Area\ of\ each\ section =\frac{6(14z-9)}{6}\\\\Area\ of\ each\ section = 14z - 9$

Thus area of each section is 14z - 9

Answer 2

The expression to denote the area of each section would be:

$14z - 9$

Given that,

The expression for the area of plot $= 84z - 54$

The number of equal sections in which it is divided $= 6$

To find,

The expression for each section = ?

The area of each section $= \frac{total area of the garden plot}{number of equal sections}$

$= \frac{84z - 54}{6}$

$= \frac{6(14z - 9)}{6}$

$= 14z - 9$

Thus, $14z - 9$ is the expression that would represent every section's area.

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