2. OBJECTIVES:
At the end of the lesson, the students will…
• Write the joint variation equation and;
• Solve problems involving joint variation
3. JOINT VARIATION
Given more than two quantities x, y,
and z, y is jointly proportional to x and z
or y varies jointly as x and z is expressed
mathematically as
y=kxz
Where k is the constant of variation
3
4. EXAMPLE 1
Express the following variation statements into algebraic
equations:
a. The number of kids n to the number of balloons
b, and toys t. n=kbt
b. The production time of a good t to the number of goods
produced g, and production expense e. t=kge
5. If y varies jointly as x and z, given y=12 when
x=3 and z=2, find the constant of variation k and
write the joint variation equation.
5
Example 2
6. EXAMPLE 3
6
If y varies jointly as x and z,
given y=48 when x=6 and z=2,
find y if x=4 and z=7.
