Page 175 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes Hence, we can write
1 1
2 2 = 1
5 x

2x + 10 = 5x

10 1
or x = 3 hours.
3 3

1
Thus, the new machine will copy 10,000 papes in 3 hours.
3

1
(ii) Number of pages copied by old machine = 3 10000 6000.
5

3
Number of pages copied by new machine = 3 10000 9000.
10

Example
A retailer purchases two types of tea priced at 120 and 160 per kg. He wants to sell the mixture
of these two types of tea at a price of 150 per kg. How much of each should be used to produce
200 kgs of mixture so that there is no change in his revenue?

Solution:
Let x be the quantity of 120 per kg. tea used then 200 - x will be the quantity of 160 per kg tea.
120x + 160(200 – x) = 150 × 200

120x + 3200 – 160x = 30000
40x = 2000
x = 50
Thus, the retailer should use 50 kg of tea priced at 120 per kg and 150 kg of sugar priced at 160
kg.

Example
The total cost of manufacturing x units of a product is assumed to be linear. It consists of a fixed
cost plus a variable cost. If the total cost of manufacturing 200 units is 5,000 and total cost of
manufacturing 400 units is 8,000, find the cost function. What is the fixed cost of production?
Solution:
Let C be the total cost and x be the number of units manufactured. It is given that C = 5,000 when
x = 200 and C = 8,000 when x = 400.
Since the cost function is assumed to be linear, therefore we have to find the equation of a
straight line passing through the points (200, 5000) and (400, 8000).

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