GRADE 9 MATHEMATICS

1. COMBINED
VARIATION

2. Definition
The statement “z varies directly as x and
inversely as y” means 𝑧 =
𝑘𝑥
𝑦
, or 𝑘 =
𝑧𝑦
𝑥
,
where k is the constant variation.

3. TRANSLATING STATEMENT TO EQUATION
Translating statements into mathematical equations using k as the constant of
variation.
a. T varies directly as a and inversely as b
𝑇 =
𝑘
𝑎
b. Y varies directly as x and inversely as the square of z
𝑌 =
𝑘𝑥
𝑧2

4. Translate each statement into mathematical equation.
1. W varies jointly as c and the square of a and inversely as b
2. P varies directly as the square of x and inversely as s
3. The electrical resistance R of a wire varies directly as its length and
inversely as the square of its diameter d
4. The acceleration A of a moving object varies directly as the
distance d it travels and inversely as the square of the time t it
travels
5. The pressure P of a gas varies directly as its temperature t and
inversely as the volume V
𝑾 =
𝒌𝒄𝒂𝟐
𝒃
𝑷 =
𝒌𝒙𝟐
𝒔
𝑹 =
𝒌𝒍
𝒅𝟐
𝑨 =
𝒌𝒅
𝒕𝟐
𝑷 =
𝒌𝒕
𝒗
ACTIVITY

5. EXAMPLE 1
If z varies directly as x and inversely as y, and z = 9 when x = 6 and y = 2.
Find z when x =8 and y = 12.
Solution:
𝑧 =
𝑘𝑥
𝑦
9 =
6𝑘
2
9 = 3𝑘
𝑘 = 3
𝑧 =
3𝑥
𝑦

6. EXAMPLE 1
If z varies inversely as x and inversely as y, and z = 9 when x = 6 and y = 2.
Find z when x =8 and y = 12.
Solution:
𝑧 =
3𝑥
𝑦
𝑧 =
3(8)
12
𝑧 =
24
12
𝑧 = 2

7. EXAMPLE 2
If s varies directly as r and inversely as t, and s=15 when r=20 and t=40, find s
when r=12 and t=20.
Solution:
𝑠 =
𝑘𝑟
𝑡
𝑘 =
𝑠𝑡
𝑟
𝑘 =
(15)(40)
(20)
𝑘 =
600
20
𝑘 = 30
𝑠 =
30(12)
20
𝑠 =
360
20
𝑠 = 18