Algebra with Whole Numbers

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Algebra with Whole Numbers

• Word Problems

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Exercise 9
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4. The diagram shows that a rectangular paddock
has a length of x metre and a breadth of y
metre. It is enclosed by a fence apart from 4
gates (one on each side of the paddock) each z
metre long. Find (in terms of x, y and z)

• a. the perimeter of the paddock.
• b. the length of the fence which encloses
  the paddock.

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a. the perimeter of the paddock.
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b. the length of the fence which encloses
the paddock.
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The diagram shows that the length of a rectangle,
2x cm, is twice its breadth, x cm.

• a. Find its perimeter (in terms of x).
• b. Find x if its perimeter is 24 cm.
• c. Hence state (in cm) the length and breadth
  of the rectangle.

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a. Find its perimeter (in terms of x).
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b. Find x if its perimeter is 24 cm.
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c. Hence state (in cm) the length and breadth
of the rectangle.
Length 8 cm Breath 4 cm
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6. The diagram shows the wire framework of a
cuboid. Its height is x cm, its breadth is 4
times its height, 4x cm, and its length is 5
times its height, 5x cm.

• a. Find (in terms of x) the total length of wire
  used to make the cuboid.
• b. Find x if the total length of wire used is 200
  cm.
• c. Hence state (in cm) the height, breadth and
  length of the cuboid.

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a. Find (in terms of x) the total length of wire
used to make the cuboid.

• 40x

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b. Find x if the total length of wire used is 200
cm.

• 40x 200
• x 5 cm

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c. Hence state (in cm) the height, breadth and
length of the cuboid.

• Height 5 cm
• Breath 20 cm
• Length 25 cm

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7. The diagram shows a farm gate made from
tubular steel. It has a length of 12x cm, a
breadth of 5x cm and diagonal stays of length 13x
cm.

• a. Find (in terms of x) the total length of
  tubular steel used to make the gate.
• b. Find x if 1200 cm of tubular steel is used.
• c. Hence state (in cm) the length and breadth of
  the gate.

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a. Find (in terms of x) the total length of
tubular steel used to make the gate.

• 60x

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b. Find x if 1200 cm of tubular steel is used.

• 60x 1200
• x 20 cm

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c. Hence state (in cm) the length and breadth of
the gate.
Length 240 cm Breath 100 cm
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The diagram shows a prefabricated wooden truss.

• a. Find x if the horizontal length of the truss,
  from A to B, is 240 cm.
• b. Find (in terms of x ) the total length of wood
  used to make the truss.
• c. Find (in cm) the total length of wood used to
  make the truss.

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a. Find x if the horizontal length of the truss,
from A to B, is 240 cm.

• 48x 240
• x 5 cm

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b. Find (in terms of x ) the total length of wood
used to make the truss.

• 105x

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c. Find (in cm) the total length of wood used to
make the truss.
525 cm 5. 25 m
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The diagram shows a solid cuboid to have a height
of x cm, a length 3 times its height and a
breadth of twice its height.

• Find (in terms of x )
• the total length of its edges.
• its total surface area.
• its volume.

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Find (in terms of x )the total length of its
edges.

• 24x

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Find (in terms of x )its total surface area.
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Find (in terms of x ) its volume.