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Pro-Print hires out photocopying machines and offers three contract options - NSC Mathematical Literacy - Question 3 - 2019 - Paper 2
Question 3
Pro-Print hires out photocopying machines and offers three contract options. The three contract options are shown in the graph on the ANSWER SHEET. Use the informat... show full transcript
Worked Solution & Example Answer:Pro-Print hires out photocopying machines and offers three contract options - NSC Mathematical Literacy - Question 3 - 2019 - Paper 2
Step 1
3.1.1 Write down the number of pages at the point where Contract 2 and Contract 3 cost the same.
Answer
To find the point where Contract 2 and Contract 3 cost the same, locate the intersection point of the two lines in the graph provided on the ANSWER SHEET. From the graph, it can be observed that both contracts are equal at 600 pages.
Step 2
Step 3
Determine which contract will be the cheapest option.
Answer
Using the calculated costs for Contract 2 and Contract 3 at 1 500 copies:
- Contract 2 cost (using the identified formula): Substituting 1500 into the formula gives: Total Cost = R625 + (R0.25 * (1500 - 600)) = R625 + R225 = R850.
- Contract 3 cost: According to the graph, the total cost remains constant after a certain number of pages. Thus, Contract 3 would be evaluated at the point determined in 3.1.1. Given the calculations, Contract 2 offers a cheaper option than Contract 3.
Step 4
3.1.3 Use the graph on the ANSWER SHEET to determine a formula for calculating the total cost (in rand) for contract 2.
Answer
The formula for Contract 2 can be derived from the graph, which shows a stepped rate system. For the first 600 copies, the fixed price is R625, and for each additional page beyond 600 pages, the cost increases by R0.25 per page. Thus, the formula can be expressed as:
Total Cost = 625 + 0.25 * (N - 600) for N > 600, where N is the number of pages.
Step 5
Draw on the same grid on the ANSWER SHEET another line graph to show the costs charged by Copy King.
Answer
To represent Copy King’s charges on the graph, a straight line should be drawn starting from the origin (0,0) with the slope indicating R0.70 per page. The line will have the equation: Total Cost = 0.70 * N, where N is the number of pages. This line will intersect the y-axis at R0 when no copies are made and will increase linearly.