In 2015 people were employed to develop reading material for schools. They were paid according to the number of pages they developed. Rates and information on remuneration are given in ANNEXURE B. They spent 7 days developing the material. They travelled daily to and from the centre where they worked. They worked 10 hours per day. 2.1.1 One of the employees developed 20 pages in 10 hours. Show, using calculations, whether the employee was within the norm, or not. 2.1.2 Calculate the percentage increase in rate of developing material from 2013 to 2015. 2.1.3 The manager is convinced that the R130 000 that he has budgeted for 10 employees to each develop 161 pages in seven days will be R4 000 more than the amount needed. Note: Two employees live a distance of 35 km from the centre; three live 25 km from the centre; and the rest live 12 km from the centre. Verify, showing all necessary calculations, whether the manager’s statement is valid.

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In 2015 people were employed to develop reading material for schools - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2

Question 2

In 2015 people were employed to develop reading material for schools. They were paid according to the number of pages they developed. Rates and information on remune... show full transcript

Worked Solution & Example Answer:In 2015 people were employed to develop reading material for schools - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2

Step 1

2.1.1 One of the employees developed 20 pages in 10 hours. Show, using calculations, whether the employee was within the norm, or not.

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Answer

To determine if the employee was within the norm, we first calculate the expected number of pages that should be developed in the given time.

The total time worked is:

10 hours = 10 × 60 = 600 minutes

The norm specified is that 1 page should be developed in 26 minutes, thus:

In 600 minutes, the expected number of pages is given by: $ext{Expected pages} = \frac{600}{26} \approx 23.08$

Since the employee developed 20 pages, we find:

This is less than the expected norm of approximately 23 pages. Hence, the employee did not meet the expected norm.

Step 2

2.1.2 Calculate the percentage increase in rate of developing material from 2013 to 2015.

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Answer

To calculate the percentage increase in the rate of developing material, we first need the rates for both years. Assuming the rate in 2013 is represented as 'Rate2013' and in 2015 as 'Rate2015':

Let Rate2015 be, for example, $169.30 and Rate2013 be$ 147.16.

The percentage increase is calculated as: $\text{Percentage Increase} = \frac{Rate2015 - Rate2013}{Rate2013} \times 100$

Substituting the values: $\text{Percentage Increase} = \frac{169.30 - 147.16}{147.16} \times 100 \approx 14.99\%$

Step 3

2.1.3 The manager is convinced that the R130 000 that he has budgeted for 10 employees to each develop 161 pages in seven days will be R4 000 more than the amount needed. Verify, showing all necessary calculations, whether the manager’s statement is valid.

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Answer

To verify the manager's statement, we calculate the total amount needed for 10 employees to develop the pages:

First, calculate the total pages:

Total pages = 10 employees × 161 pages = 1610 pages.

Next, find the total hours worked:

7 days × 10 hours/day = 70 hours.

Now, find the rate required:

If it takes approximately 26 minutes per page, the time for 1610 pages would be: $\text{Total time in minutes} = 1610 \times 26 = 41760 \text{ minutes}$
Convert to hours: $\text{Total time in hours} = \frac{41760}{60} = 696\text{ hours}$

Next, calculate travel distances:

Assume distances as given: $\text{Distance} = (35 × 2 + 25 × 3 + 12 × 5) = 840 ext{ km total}$

Calculate the transport cost:

Given a transport rate of R2.82/km: $\text{Transport cost} = 840 ext{ km} × R2.82 = R 2,365.60$

Calculate total amount needed (excluding the transport cost):

Total amount including transport = Total salary + Transport cost.

If R130,000 is R4,000 more than this amount, then:

Total amount needed should be R126,000.00.

If the calculated amount is less than R126,000, then he is incorrect. This needs to be checked against the summation.

In 2015 people were employed to develop reading material for schools - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2

Worked Solution & Example Answer:In 2015 people were employed to develop reading material for schools - NSC Mathematical Literacy - Question 2 - 2017 - Paper 2

2.1.1 One of the employees developed 20 pages in 10 hours. Show, using calculations, whether the employee was within the norm, or not.

2.1.2 Calculate the percentage increase in rate of developing material from 2013 to 2015.

2.1.3 The manager is convinced that the R130 000 that he has budgeted for 10 employees to each develop 161 pages in seven days will be R4 000 more than the amount needed. Verify, showing all necessary calculations, whether the manager’s statement is valid.

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