Question

1. Quickfence Ltd has the following method for calculating the price it will charge to put up a new fence:

• Labour is charged at $25 per hour, or part of an hour. It takes 45 minutes of labour per metre to put up a new fence.
• Fence panels are 2 m long and cost $20 each. If they have to be cut, the price of a full panel is charged.
• Fence posts cost $5 each. A post is needed between fence panels and at both ends.

What will be the price for a fence 13 m long?

2. A farmer is planning to create a temporary ‘pen’ for livestock, by cutting a large section of plastic netting into strips, joining the strips together and then fixing the combined length to posts. He decides the fence must be 2 m high, and must form a shape that is nearly square: either a precise square or a rectangle whose length and width do not differ by more than 5 m.

If the length and width are both whole numbers of metres, what is the greatest area than can be created from 156 m2 of netting?

Answer 1

Step-by-step explanation:

1)

Labour:

For 1m, 45 mins of labour

For 13m, there will be 13*45 = 585 mins of labour = 9.75 hours of labour

Since 1 hour of labour costs $25

And part of and hour also costs $25

Cost of labour = (25*9) + (25*1) = $250

Fence panels:

One 2m long fence panel costs $20

Less than 2m fence panel also costs $20

For 13m panel, 13/2 (6.5 ~ 7 panels) will be used

Since half a panel also costs $20, there fore the total of fence panels will cost 7*20 = $140

Fence posts:

Since 7 panels are used,

A post costs $5 each

And posts are required between fence panels and at both ends,

8 posts will be used

Which will cost 8*5 = $40

Therefore the total price = 250+140+40 =$430