Beginning and Intermediate Algebra - Wallace Math Courses ...

The formula for the area of a triangle has three variables in it. If we divide the
area by the base times the height we will also get a constant, 1
. This relationship
2
is called joint variation or jointly proportional. If we see this phrase in the
problem we know to divide the first variable by the product of the other two to
find the constant of variation.
Example 94.
A varies jointly asxand y ′′ Jointly ′′ tells us to divide by the product
A
=k Our formula for the relationship
xy
Once we have our formula for the relationship in a variation problem, we use
given or known information to calculate the constant of variation. This is shown
for each type of variation in the next three examples.
Example 95.
Example 96.
Example 97.
w is directly proportional to y and w = 50 when y =5
w
y =k ′′ directly ′′ tells us to divide
(50)
=k
(5)
Substitute known values
10 =k Evaluate to find our constant
c varies indirectly as d and c=4.5 whend=6
cd =k ′′ indirectly ′′ tells us to multiply
(4.5)(6) =k Substitute known values
27 =k Evaluate to find our constant
x is jointly proportional to y andz and x = 48 when y = 2 and z = 4
x
yz =k ′′ Jointly ′′ tells us to divide by the product
(48)
=k
(2)(4)
Substitute known values
6 =k Evaluate to find our constant
58