Page 21 - Mathematics_Form_Two

Rates and variations

Using t = 5 and c = 20, then Example 1�17
20
___
5 = The monthly rent for an apartment varies
d directly with its area and inversely with
5d = 20
the number of roommates. If Tsh 400,000
d = 4 is the rent for an apartment of 900 square
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Therefore, it will take 4 days for 5 tailors units with 3 roommates, find the rent for
to sew 20 clothes. an apartment of 1,200 square units with
4 roommates.
Example 1�16
Solution Mathematics for Secondary Schools
The cost of a certain material varies Given R ∝ a and R ∝ 1 , then
directly with the quantity purchased and a a n
inversely with the number of suppliers. R ∝ ⇒ R = k
If the cost is Tshs 120,000 when the n n
quantity is 100 units and there are 4 k = R×n
suppliers, find the constant of variation a
and the cost when the quantity becomes When R = Tshs 400,000 n = 3, and
150 units and there are only 3 suppliers. a = 900 , it follows that
400000 3×
Solution k =
Let C be the cost of materials q be the 900
quantity purchased, and S be the number =1333.33
of suppliers. Now, for a = 1200 and n 4,
=
1
Thus, C ∝ and C ∝ . The combined R = 4000 1200× = 400,000
q
variation is: S 34×
q q Therefore, the rent for the apartment
C ∝ ⇒ C = k will be Tshs 400,000.
S S

Exercise 1�5
Given C = Tshs 120,000 , q = 100 ,
S = 4 , then 1. If y varies directly as the square
of x and inversely as z, find the
CS 120000 4× percentage change in y when x is
k = = = 4,800
q 100 increased by 10% and z is decreased
by 20%.
3
Now, if S = and q = 150 , it follows
that 2. Suppose P varies directly as V and
inversely as the square root of R. If
4800 150×
C = = 240,000 P = 180 when R = 25 and V = 9,
3 find the value of P when V = 6 and
Therefore, the cost of materials will be R = 36.
Tshs 240,000.

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 15