Page 20 - Mathematics_Form_Two

Rates and variations

ky
__
Given d = 52 days, h = 8 hours, w = 9 x = . It implies that
z
1
1
1
employees, w = 13 employees, and x z x z
2
1 1
=
2 2
h = 6 hours, then _ _ = k
2 y y
d 2
2
1
___
6 __
9 ___
= × ,
13 8 52 Given x = 8, y = 12,
1
1
9 × 52 × 8

_________
2
1
d = 48 days. . z = 6, y = 16 and z = 4, then
FOR ONLINE READING ONLY
2
d =
x z y
13 × 6
2
______
Mathematics for Secondary Schools Therefore, it will take 48 days for 13 Therefore, the value of x is 16.
1 1 2
x =

y z
2
1 2

2
8 × 6 × 16
_________
=

12 × 4
employees to complete the piece of work.
= 16
Combined variations
Consider the formula used to evaluate a
person’s body mass in relation to his/her
height. The value obtained is called Body Example 1�15
Three tailors can sew 15 clothes in 5
Mass Index (BMI) and it is given by the days. How long will it take 5 tailors
formula working at the same rate to sew 20
mass clothes?
Body Mass Index (BMI) =
height 2 Solution
In this formula, BMI varies directly with Let t, d and c represent the numbers of
mass and inversely with the square of the
height of the person. This relationship is tailors, days, and clothes, respectively.
known as a combined variation. The number of tailors is inversely
Thus, combined variation involves a proportional to the number of days, that
1 __
variable that varies both jointly and is, t ∝ and is directly proportional
d
inversely with other variables. That is, to the number of clothes, that is, t ∝ c.
it is a combination of direct and inverse Combining the two proportions gives,
variations. c __
∝
t .
d
The variation equation is then given as
Example 1�14 t = k
c __
If x varies directly as y and inversely as d
z , and x = 8 when y = 12 and z = 6 , find The value of k is computed as follows:
the value of x when y = 16 and z = 4. Given t = 3, d = 5, and c = 15 ,
td __
Solution k =
c
If x varies directly as y and inversely = _____
3 × 5

proportional as z, that is, x ∝ y and 15
1 __
x ∝ . The combined variation becomes = 1
z
c __
y So, the variation equation is t = .
__
x ∝ . The variation equation is given by; d
z
14
Student's Book Form Two
11/10/2024 20:11:10
MATHEMATIC F2 v5.indd 14
MATHEMATIC F2 v5.indd 14 11/10/2024 20:11:10