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Calculate the total cost for 2019 m of fencing using 5m rolls costing R162.50 each. 1.3) Determine the number of fence poles needed for 2019 m of fencing with 4.8 m spacing. 1.4) Calculate the cost

Mathematics

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3 parts
1.2

R65650.00

1.3

422 poles422 \text{ poles}

1.4

R35196.00

Step-by-step solution

7 steps

Here are the solutions to your questions:

Part 1.2· 2 steps

  1. Determine the number of 5m rolls needed for 2019 m2019 \text{ m} of fencing.

    Number of rolls=Total lengthLength per roll=2019 m5 m/roll=403.8 rolls\text{Number of rolls} = \frac{\text{Total length}}{\text{Length per roll}} = \frac{2019 \text{ m}}{5 \text{ m/roll}} = 403.8 \text{ rolls}

    Since you cannot buy a fraction of a roll, you must purchase 404 rolls to cover the entire length.

  2. Calculate the total cost.

    Total cost=Number of rolls×Cost per roll\text{Total cost} = \text{Number of rolls} \times \text{Cost per roll} Total cost=404×R162.50=R65650.00\text{Total cost} = 404 \times R162.50 = R65650.00

    The final answer is R65650.00\boxed{R65650.00}.

Part 1.3

422 poles422 \text{ poles}

Assumption: The "Maximum space of 4.8cm" is a typo and should be 4.8 m4.8 \text{ m}, as 4.8 cm4.8 \text{ cm} is impractical for fence pole spacing. We will use 4.8 m4.8 \text{ m} spacing.

  1. Calculate the number of intervals for the 2019 m2019 \text{ m} fence with 4.8 m4.8 \text{ m} spacing.

    Number of intervals=Total lengthSpacing=2019 m4.8 m/interval=420.625\text{Number of intervals} = \frac{\text{Total length}}{\text{Spacing}} = \frac{2019 \text{ m}}{4.8 \text{ m/interval}} = 420.625
  2. Determine the number of poles.

    For a linear fence, the number of poles is the number of intervals rounded up, plus one for the starting pole.

    Number of poles=⌈420.625⌉+1=421+1=422 poles\text{Number of poles} = \lceil 420.625 \rceil + 1 = 421 + 1 = 422 \text{ poles}

    The final answer is 422 poles\boxed{422 \text{ poles}}.

Part 1.4R35196.00

  1. Calculate the cost if poles are bought in groups of 6 and individually for the remainder.

    Total poles needed: 422.
    Number of groups of 6:

    Number of groups=4226=70 with a remainder of 2\text{Number of groups} = \frac{422}{6} = 70 \text{ with a remainder of } 2

    So, 70 groups of 6 poles will be bought, and 2 poles will be bought individually.
    Cost for groups: 70×R500=R3500070 \times R500 = R35000.
    Cost for individual poles: 2×R98.00=R196.002 \times R98.00 = R196.00.
    Total cost (groups + singles): R35000+R196.00=R35196.00R35000 + R196.00 = R35196.00.

  2. Calculate the cost if all poles are bought individually.

    Total cost (individually)=422×R98.00=R41356.00\text{Total cost (individually)} = 422 \times R98.00 = R41356.00
  3. Compare the costs.

    The cost of buying in groups and remaining singles (R35196.00R35196.00) is less than buying all individually (R41356.00R41356.00).
    The final answer is R35196.00\boxed{R35196.00}.

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