Practice Tasks

Rosemary wants to find the cheapest rental van for the trip to their 5-day Netball tournament. The Hire-a-Van Company has three plans.

The graphs of Plan A and Plan B are drawn on the grid below.

Plan C is $50 per day plus 25c per kilometre.

For a 5-day trip Plan C can be described by the equation:

C = 0.25k + 250

Where C is the cost of the 5-day trip in dollars

and k is the number of kilometres travelled on the 5-day trip.

1) Draw the graph of Plan C on the same grid as above: C = 0.25k + 250

2) Write the equations for Plan A and Plan B

Plan A C =

Plan B C =

3)Which plan would be best if they only traveled exactly 400km?

4) Which plan would be best if they traveled exactly 1200km?

5) Rosemary needs to make recommendations to other teams coming to the tournament about the best deal. Make a recommendation that covers travel from 0 to 1200km.

6) Another competitor, “Rent a Van” also wants to suggest 3 plans. What plans should they give, so that they better (undercut) Hire a Van’s three plans. Clearly explain why “Rent a Van” is better.

Frank sells various items online using the “tradeit” website. He is required to send items all around the country and likes to spend as little as possible on postage so he can make a bigger profit. There are three different postage companies he could go with, each company works out the cost depending on the weight of the package. He sends a variety of items, the heaviest item he sells is 12kg.

Task

1. Represent the three shipping companies using three equations and graphs (with the same variables and scale).

2. If Frank sends a parcel weighing 6kg what is his best option and why?

3. Design a guide for Frank so he can easily see what company is cheapest for the items he sends.

4. A new company Discount Deliveries is entering the market and wants to charge as much as possible yet still be priced below all other companies. What would you recommend they charge?

There are 3 computer repair companies in town. Time for repair is charged at an hourly rate (fractions of hours are charged at the same rate). Some companies also charge a call out fee.

1. Create an equation for each company and plot them on a graph.

2. Which computer repair business offers the cheapest rate, if the job is to take 5 hours?

3. Find when the cost is the same for Delta computers and clockwise computers?

4. You are planning to go into the computer repair business in competition with Clockwise, Dellta and Espom. Create your own piecewise function that only just undercuts all 3 businesses.

1. Draw a graph to show the three contracts giving the equation of each line.

2. List, in order, the cost to Farmer Brown if she wants to have her herd off farm for 19 weeks.

3. Design a pricing guide for Farmer Brown to ensure he always gets the best price.

4. If you wanted to undercut Grasslands, Rent-a-Block and Grassdowns, develop equations for your own contract.

Freyberg is connected to the outside world by a fibre optic cable that goes underground behind the maths classrooms in J block, crosses the rugby field and comes up in the grounds of Palmerton North Hospital. This task is built around putting this cable in. Three companies are asked to tender and the each have a different approach to such jobs on is clearly very keen and one may not be too interested in installing cables under 4000m long. We assume that the following ideas apply to cables up to 4000m in length.

1. Draw a graph to show the three contracts costs for cables up to 4000m.

2. List, in order, the cost to Freyberg for a cable 840m long.

3. Find the conditions when Little Holes and Takes Weeks would both cost the same.

4. If you wanted to undercut the three companies for jobs with cable length between zero and 4000m, develop equation(s) for your own contract.

Paul’s parents are going to put on a party for his 21^st birthday. They have decided to compare the charges of three venues: Eden Golf Club, Fraser Squash Club and Georgetown Rugby Club.

They have done some research and have the following information for each venue:

1. Represent the three venue charges using the same representation, for example, three equations or three graphs with the same variables and scale.

2. Paul would like to have 60-80 guests, which venue is his best option and why?

3. His parents would like it to be a smaller gathering of a maximum of 50 people, which venue is best and give reasons why.

Task:

1. Graph the above information and give the equation for the cost of each company over a period of 6 hours.

2. When is the value of Pete and Lee’s services the same?

3. When job has taken 4 hours find the value that each plumber would charge and list them in order from cheapest to most expensive.

4. Another plumber is starting up a business and wants to undercut the 3 other plumbers by using a simple rule. Form an equation that would achieve this for him.

#1 Netball Trip

#2 Postage Problem Answers

#3 Computer Repair Answers

#4 Wintering over a Dairy Herd

#5 The Blue Pipe

#6 Paul's Birthday Problem

#7 Plumber's Pricing