Lesson Worksheet: Joint Variation Mathematics • 9th Grade

In this worksheet, we will practice writing an equation to describe joint variation and using proportions to find other sets of values to solve real-world problems.

Q1:

𝑦 varies jointly as 𝑥 and 𝑧. If 𝑦=15 when 𝑥=9 and 𝑧=8, find 𝑦 when 𝑥=16 and 𝑧=9.

Q2:

𝑦 varies jointly as 𝑥 and the cube root of 𝑧. If 𝑦=120 when 𝑥=5 and 𝑧=8, find 𝑦 when 𝑥=10 and 𝑧=64.

Q3:

𝑦 varies jointly as 𝑥 and the square of 𝑧. If 𝑦=18 when 𝑥=2 and 𝑧=3, find 𝑦 when 𝑥=6 and 𝑧=7.

Q4:

Given that 𝑧 varies jointly with 𝑥 and 𝑦, such that 𝑧=12𝑥𝑦, find 𝑥 when 𝑦=1 and 𝑧=2.

  • A𝑥=14
  • B𝑥=1
  • C𝑥=2
  • D𝑥=12
  • E𝑥=4

Q5:

A quantity 𝑥 varies directly with 𝑦 and inversely with 𝑧. Given that 𝑘 is the constant of variation, find the equation that models 𝑥.

  • A𝑥=𝑧𝑦
  • B𝑥=𝑦𝑧
  • C𝑥=𝑘𝑧𝑦
  • D𝑥=𝑘𝑦𝑧
  • E𝑥=𝑘𝑦𝑧

Q6:

True or False: If 𝑧 varies jointly with 𝑥 and 𝑦, and 𝑧=40 when 𝑦=2 and 𝑥=4, then the constant of variation equals 5.

  • ATrue
  • BFalse

Q7:

Given that 45𝑥6𝑦3𝑥6𝑧=𝑦𝑧 and 𝑥, which of the following relations is correct?

  • A𝑦𝑧
  • B𝑦1𝑧
  • C𝑦𝑧
  • D𝑦1𝑧

Q8:

A variable 𝑧 varies jointly with variables 𝑥 and 𝑦. Given that 𝑧=12 when 𝑦=2 and 𝑥=3, write the equation that describes how 𝑧 depends on 𝑥 and 𝑦.

  • A𝑧=4𝑥𝑦
  • B𝑧=3𝑥𝑦
  • C𝑧=2𝑥𝑦
  • D𝑧=12𝑥𝑦
  • E𝑧=6𝑥𝑦

Q9:

True or False: Given that 𝑦 varies jointly with 𝑥 and 𝑧 such that 𝑦=2𝑥𝑧, 𝑦=12 when 𝑥=2 and 𝑧=3.

  • ATrue
  • BFalse

Q10:

When a body is moving onward, its kinetic energy 𝑇 varies jointly with mass 𝑚 and the square of velocity 𝑣. If 𝑇=9J when 𝑚=2kg and 𝑣=3/ms, find 𝑣 when 𝑇=4J and 𝑚=2kg.

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