Using and Managing Data and Information

Task 1:

1. 8 people can paint a fence in 3 hours. How long will it take 12 people to paint the same fence (Assume everyone works at the same rate). You must show all your workings.
2. A tyre dealer sells 510 standard tyres in July generating revenue of £25,500. How much revenue is generated the following month, with the same unit price if 670 tyres are sold? You must show all your workings.
3. 12 men take 5 days to build a road 200m long. How many days will 20 men take to make a similar road which is 400m long? Explain your answer in detail.
4. Super Paint is mixed by using yellow and blue in a ratio of 7:2
   1. How much yellow and how much blue must be used to make 72 litres of the super paint?
   2. How much blue is used if 35 litres of yellow is used?

Task 2:

1. How many combinations of 4 students can be made from a class of 30 students? Show all your workings.
2. How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9 inclusive? Show all your workings.
3. You consider entering a Lottery, where you choose six different numbers between 1 to 50 inclusive. Explain how you would calculate the possible combinations of winning the jackpot (i.e., obtaining all six numbers).

Task 3:

1. Steven receives an electricity bill for £90. The bill includes a quarterly charge of £15 and the cost per unit is 6 pence. Calculate to the nearest whole number, the number of units he has used.
2. A first-time house buyer can make 360 monthly payments of £480 to repay the mortgage. How many monthly payments are required if he can pay £450 per month?
3. A second-hand car dealer offered a 20% discount for a car, with a sales price of £6,400 for immediate cash sales. What was the original price before the discount?

Task 4:

1. The equation of a line is given as y = 5x + 8
   How is the value 5 calculated?
2. In the diagram below:
   • Find the gradient of line
   • Write the equation of the line in the form y = mx + b
   • Find the exact value of y when x is 6


3. Explain your methods clearly.

Task 5:

In this task, you are asked to formulate the linear programming problem below and then solve it.

A sub-contractor produces two types of units for a kitchen manufacturer, a base unit (B) and a cabinet unit (C).

The base unit requires 15 minutes in the production department and 40 minutes in the assembly department.

The cabinet unit requires 20 minutes in the production department and 30 minutes in the assembly department.

The production and assembly of these two units are done by specialist carpenters who are in short supply. Each day only 5 hours in the production department are available and only 10 hours are available in the assembly department.

Once sold, the base units contribute £5 to profit and the cabinet units £3 to profit.