The statement “t varies directly as x and inversely as y”

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!!!