Question of Variations

1. A computer company develops a new scan disk. The cost $P of producing a scan disk is partly constant and partly varies inversely as the total number of scan disks N produced. When 2500 scan disks are produced, the total cost is $225 000. When 5000 scan disks are produced, the total cost is $425 000.
(a) Find the cost of producing a scan disk if 2500 scan disks are produced.
(b) Express P in terms of N.
(c) If the selling price of a scan disk is $120, find the profit percentage if the company products and sells 1000 scan disks.
(Give the answer correct to 3 significant figures.)
(d) If the selling price of a scan disk is $100, what is the minimum number of disks that need to be produced in order to make a profit?

2. The school soccer team organizes a soccer training camp. The school subsidizes two-thirds of the total expenses and the team members share the remaining expenses. The total expense $E for the camp is partly constant and partly varies directly as the number of team members N joining the camp.
If 15 members join the camp, the school has to pay $2400.
If 20 members join the camp, the school has to pay $3000.
(a) What is the total expense if 20 members join the camp?
(b) Express E in terms of N.
(c) If 30 members join the camp, how much should each member pay?
(d) If each members pays $72, how many members joined the camp?