Joint And Combined Variation Worksheet Kuta [work] ◎

( y ) varies jointly with ( x ) and the square of ( z ), and inversely with ( w ). If ( y = 20 ) when ( x = 4, z = 2, w = 3 ), find ( y ) when ( x = 5, z = 3, w = 5 ).

This is essentially "direct variation" but with more friends. One variable depends on the product of two or more others. Formula: Real World: The area of a triangle ( ) varies jointly as the base and height. joint and combined variation worksheet kuta

[ y = kxz ] Where ( k ) is the constant of variation. You read this as: "y varies jointly as x and z." ( y ) varies jointly with ( x

Try these. Answers are at the bottom.

Do not skip finding ( k ). Beginners often try to set up a proportion directly — that only works for single direct or inverse. For joint/combined, always find ( k ) first. One variable depends on the product of two or more others

Some Kuta problems involve squares or square roots (e.g., " varies inversely as the square of

This is where most Kuta worksheets begin. Here is the key difference between the two: