This document discusses combined variation and how to solve problems involving quantities that vary directly and inversely with other variables. It provides examples of translating statements of combined variation into mathematical equations. It also works through an example problem, showing how to solve for an unknown variable value when the quantities it varies with are given. The document concludes by instructing the reader to practice additional combined variation problems from their workbook.

1. Prepared by:
REYBETH D. RACELIS, LPT
COMBINED
VARIATION

2. OBJECTIVES
Translates the given variation
statement into mathematical
equation.
Solves problems involving
combined variation.

3. COMBINED VARIATION
The statement “t varies directly as
x and inversely as y”
In symbol:
t = kx/y , k = ty/x where k is the
constant of variation.

4. Translates the following statement into
mathematical equation.
 T varies directly as a and inversely b. T =ka/b
 Y varies directly as x and inversely as the square of z.
Y=kx/z²
 P varies directly as the square of x and inversely as s.
P=kx²/s
 The time t required to travel is directly proportional to the
temperature T and inversely proportional to the pressure P.
t=kT/P
 The pressure P of a gas varies directly as its temperature t
and inversely as its volume V. P=kt/V

5. Problem Solving
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.

6. Solution:
z = kx/y z = 3x/y
9 = k(6)/2 z = 3(8)/12
9 = 6k/2 z = 24/12
2(9) = 6k z = 2
18 = 6k
k = 3

7. GENERALIZATION:
How do you solve
problems involving
combined variation?

8. EVALUATION
Perform Activity 21
Letter A #1-5 and Letter
B #1 a-c only, LM page
221

9. THANK YOU
for your
cooperation and
participation!!!