Given that y varies jointly as x and x and y= 64 when x= 4 and z= 8, find y when x= 8 and z= 6.

Question:

Given that y varies jointly as x and x and y= 64 when x= 4 and z= 8, find y when x= 8 and z= 6.

Joint Variation:

One variable can be directly proportional to two variables at the same time. If we have a which varies jointly with b and c, the relationship between the three is written as:

$$a\propto bc $$

Answer and Explanation:

As y varies jointly as x and z, we can write the relationship as:

$$y=kxz $$


As y= 64 when x= 4 and z= 8, the value of k is found as follows.

$$\begin{align} 64&=k*4*8\\ k&=2 \end{align} $$


Now, the value of y when x= 8 and z= 6 will be:

$$\begin{align} y&=2*8*6\\ &=96 \end{align} $$


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Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23
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