Write a joint variation equation

1
EXAMPLE 5
Write a joint variation equation
The variable z varies jointly with x and y. Also,
z 75 when x 3 and y 5. Write an equation
that relates x, y, and z. Then find z when x 2
and y 6.
SOLUTION
z axy
75 a(3)(5)
Substitute ?75 for z, 3 for x, and 25 for y.
75 15a
Simplify.
5 a
Solve for a.
2
EXAMPLE 5
Write a joint variation equation
z 5xy
z 5xy 5(2)(6) 60
3
EXAMPLE 6
Compare different types of variation
Write an equation for the given relationship.
Relationship
Equation
a. y varies inversely with x.
b. z varies jointly with x, y, and r.
z axyr
c. y varies inversely with the square of x.
d. z varies directly with y and inversely
with x.
e. x varies jointly with t and r and
inversely with s.
4
for Examples 5 and 6
GUIDED PRACTICE
The variable z varies jointly with x and y. Use
the given values to write an equation relating x,
y, and z. Then find z when x 2 and y 5.
9. x 1, y 2, z 7
SOLUTION
z axy
5
for Examples 5 and 6
GUIDED PRACTICE
7 a(1)(2)
Substitute 7 for z, 1 for x, and 2 for y.
7 2a
Simplify.
Solve for a.
6
for Examples 5 and 6
GUIDED PRACTICE
7
for Examples 5 and 6
GUIDED PRACTICE
10. x 4, y 3, z 24
SOLUTION
z axy
24 a(4)( 3)
Substitute 24 for z, 4 for x, and 3 for y.
Simplify.
24 12a
Solve for a.
8
for Examples 5 and 6
GUIDED PRACTICE
z 2 xy
z 2 xy 2 ( 2)(5) 20
9
for Examples 5 and 6
GUIDED PRACTICE
The variable z varies jointly with x and y. Use
the given values to write an equation relating x,
y, and z. Then find z when x 2 and y 5.
11. x 2, y 6, z 18
SOLUTION
z axy
10
for Examples 5 and 6
GUIDED PRACTICE
18 a( 2)(6)
Substitute 18 for z, 2 for x, and 6 for y.
18 12a
Simplify.
Solve for a.
11
for Examples 5 and 6
GUIDED PRACTICE
12
for Examples 5 and 6
GUIDED PRACTICE
The variable z varies jointly with x and y. Use
the given values to write an equation relating x,
y, and z. Then find z when x 2 and y 5.
12. x 6, y 4, z 56
SOLUTION
z axy
13
for Examples 5 and 6
GUIDED PRACTICE
56 a( 6)(4)
Substitute 56 for z, 6 for x, and 4 for y.
56 24a
Simplify.
Solve for a.
14
for Examples 5 and 6
GUIDED PRACTICE
15
for Examples 5 and 6
GUIDED PRACTICE
Write an equation for the given relationship.
13. x varies inversely with y and directly with
w.
SOLUTION
14. p varies jointly with q and r and inversely
with s.
SOLUTION