Joint And Combined Variation Worksheet Kuta May 2026

Before you download a worksheet, you need a rock-solid conceptual foundation.

Use the first set of given values (e.g., "(y=24) when (x=2) and (z=3)"). Substitute them into your equation and solve for (k).

Example: (y) varies jointly as (x) and (z). (y=24) when (x=2, z=3). [ 24 = k \cdot 2 \cdot 3 ] [ 24 = 6k ] [ k = 4 ] joint and combined variation worksheet kuta

Joint variation is represented by the equation:

$$y = kxz$$

where $y$ varies jointly with $x$ and $z$, and $k$ is the constant of variation.

Problem:
( y ) varies directly as ( x ) and inversely as ( z ). If ( y = 8 ) when ( x = 6 ) and ( z = 3 ), find ( y ) when ( x = 10 ) and ( z = 5 ). Before you download a worksheet, you need a

Solution:
Step 1: ( y = \frack \cdot xz )
Step 2: ( 8 = \frack \cdot 63 ) → ( 8 = 2k ) → ( k = 4 )
Step 3: ( y = \frac4xz )
Step 4: ( y = \frac4 \cdot 105 = \frac405 = 8 )
Answer: ( y = 8 )