12.5 – 12.7 Variation

CA Standard 15.0Apply algebraic techniques to rate

problems.

Vocabulary

Direct Variation kxy

Constant of Variation

#1 Find an equation of variation where y varies directly as x.

12 when 84 xy

kxy

k1284

7kxy 7

#2 Find an equation of variation where y varies directly as x.

80 when 50 xy

kxy

k8050

625.0kxy 625.0

x

ky

Vocabulary

Inverse Variation

#3 Find an equation of variation where y varies inversely as x.

6.0 when 105 xy

x

ky

6.0105

k

63kx

y63

#4 Find an equation of variation where y varies inversely as x.

20 when 45 xy

x

ky

2045

k

900kx

y900

#5 Solve the problem using direct variation. The Weight (V) of an object on Venus varies

directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 150 lb on Earth weigh on Venus?

V lb 106

E lb 120

#5 Solve the problem using direct variation.

EvV ith directly w aries

150 is E when for Solve Vequationan Find

kEV

k120106

88.0k

EV 88.0

EV 88.0)150(88.0V

lb 132V

#6 Solve the problem using inverse variation.

The time (t) required to drive a fixed distance varies inversely as the speed (r). It takes 5 hours at 60 km/h to drive a fixed distance. How long would it take to drive the same distance at 40 km/h?

t hours 5r km/h 60

#6 Solve the problem using direct variation.

rvt with inversely aries 40 is when for Solve rtequationan Find

r

kt

605

k

300k

rt

300

rt

300

40

300t

hours 5.7t

kxyz

VocabularyVocabulary

• Joint Variation

#7 Find an equation of variation where #7 Find an equation of variation where ww varies jointly as varies jointly as x, y, x, y, and and zz..

6 and ,5 ,3 ,36 zyxwkxyzw

k)6)(5(336

5

2k

xyzw5

2

k9036

#8 Find an equation of variation where #8 Find an equation of variation where QQ varies jointly as varies jointly as R R and and SS..

3 and ,1 ,2 SRQ

kRSQ k)3(12

3

2k

RSQ3

2

k32

y

kxz

VocabularyVocabulary

• Combined Variation

#9 Find an equation of combined variation #9 Find an equation of combined variation where where PP varies directly as varies directly as q q and inversely as and inversely as rr..

5 and ,16 ,064.0 rqP

r

kqP

5

16064.0

k

k1632.0 02.0k

r

qP

02.0

#10 Solve the problem using #10 Solve the problem using combined variation.combined variation.

• Find an equation of combined variation where A varies directly as b and inversely as c. One set of values is A = 4, b = 12, and c = 9. Find A when b = 7 and c = 3.

c

kbA

#10 Solve the problem using #10 Solve the problem using combined variation.combined variation.

9 and ,12 ,4 cbA

9

124

k

k1236

3k

c

bA

3

3

)7(3A

3 and 7 when Find cbA

3

21A

7A

#11 Solve the problem using #11 Solve the problem using variation.variation.

• The interest earned at Whole World Savings & Loan varies jointly as the amount deposited in the bank and the time elapsed since the deposit. If a $500 deposit earns $120 interest after 3 years, how much does an $800 deposit earn after 5 years?

I 120$

D 500$t years 3

#11 Solve the problem using #11 Solve the problem using variation.variation.

tDvI and th jointly wi aries years 5after deposit 800$equationan Find

kDtI

k)3(500120

08.0k

DtI 08.0

)5)(800(08.0I

)4000(08.0I

320$Ik1500120