Page 19 - Mathematics_Form_Two

Rates and variations

y
__
The variation equation is k = , From c = kbd .
xz
where k is a constant of c = 12bd .
proportionality. Given, c = 300, b = 6,

Given x = 4, z = 2, and y = 24 it
follows that 300 12 6 d= ×× .
FOR ONLINE READING ONLY
24
k = _____ 72d = 300

4 × 2
= 3 d = 4.2
Therefore, the variation equation is Therefore, 4.2 days will be needed to
y = 3xz. bake 300 cakes or it requires 4 days, 4
(b) With y = 3xz, if x = 5 and z = 6, hours, and 48 minutes to bake 300 cakes. Mathematics for Secondary Schools
then Example 1�13
y = 3 × 5 × 6
= 90 Nine employees work 8 hours a day to
Therefore, the value of y is 90. complete a piece of work in 52 days.
How long will it take 13 employees to
complete the same work by working 6
Example 1�12 hours a day?
A bakery has a project to bake 240 cakes.
With 4 bakers working for 5 days, they Solution
can complete the task. If the number of Let w, h, and d represent the number
cakes is increased to 300 and the bakery of employees, hours, and days,
decides to use 6 bakers, how many days respectively.
will it take to bake all 300 cakes? Thus, it follows that the number of
Solution employees varies inversely as the
Let c be the number of cakes, b be the number of hours and days, that is,
number of bakers, and d be the number w ∝ and w ∝ .
1 __
1 __
of days. h d
More cakes can be produced if there are The joint variation is given by the
more bakers and more working days, relation
assuming other factors remain constant. w ∝ .
1 ___
It implies that these variables vary jointly hd
and are directly related. The variation equation is
k _
Thus, c ∝ bd . w = , where k is a constant of
hd
c = kbd . proportionality.
Thus,
Given c = 240, b = 4, and d = 5., it ____
k
implies that w =
h d
1

1
1
k
240 = 4 5 k× × w =
____
2
2
20k = 240 w h d
2
h d
2 __
2 __
___
1
k = 12 Hence, = × .
w
h d
2
1
1
13
Student's Book Form Two
11/10/2024 20:11:10
MATHEMATIC F2 v5.indd 13
MATHEMATIC F2 v5.indd 13 11/10/2024 20:11:10