Page 174 - DMTH201_Basic Mathematics-1

Unit 6: Functions

When x = 0, y = 80 and when x = 8, y = 92. The equation of a line passing through the two Notes
92 80 3 3
points is y 80 (x 0) . Thus, y 80 x or y x 80.
8 2 2
(ii) For the year 2010, x = 10.

3
y 10 80 95 crores will be the population in the year 2010.
2

Example
A cinema hall has 2000 seats and the revenue obtained from the sale of tickets in a particular
show was 62000. The price of two categories of seats were 25 and 40. Assuming that all the
seats were occupied, find the number of seats in each category.
Solution:

Let x be the number seats each with price 25, then 2000 – x will be the number of seats in the
other category. Thus, we can write
25x + 40(2000 – x) = 62000

15x = 80000 - 62000

18000
x = 1200
15
2000 – x = 2000 – 1200 = 800
Thus, the number of seats are 1200 with price 25 and 800 with price 40.

Example
An old photocopying machine can copy 10,000 pages in 5 hours. With the help of a new machine,
the job can be completed in 2 hours.
(i) How much time would the new machine require to do the job alone?
(ii) How many pages are copied by each machine when each machine is used for three hours?

Solution.
(i) Let x be the time needed for the new machine to complete the job.

1
Rate of work for the old machine units of work per hour.
5

1
Rate of work for the new machine units of work per hour
x

1 1
thus the work done by each macine in 2 hours is 2 and 2 respectively.
5 x

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