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Math Practice

Joint Variation Practice Problems

Write the variation equation, find k from the values you are given, then use it with the new values. The later problems add squares, combined variation and real formulas.

  1. 1.

    varies jointly with and , and when and . Find .

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    , so .

  2. 2.

    With , find when and .

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    .

  3. 3.

    varies jointly with and , and when and . Find when and .

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    , so .

  4. 4.

    varies jointly with and . If triples and doubles, by what factor is multiplied?

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    .

  5. 5.

    varies jointly with and the square of , and when and . Find when and .

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    , so ; then .

  6. 6.

    varies directly with and inversely with , and when and . Find when and .

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    , so ; then .

  7. 7.

    varies directly with and inversely with , and when and . Find when and .

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    , so .

  8. 8.

    varies jointly with and , and when and . What is ?

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    , so : the area of a triangle.

  9. 9.

    The cost of painting a wall varies jointly with its length and height. A 12 ft by 8 ft wall costs $192. What does a 15 ft by 10 ft wall cost, in dollars?

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    , so .

  10. 10.

    Simple interest varies jointly with principal and time. $1,000 earns $120 in 3 years. How much does $2,500 earn in 4 years at the same rate, in dollars?

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    , so .

  11. 11.

    varies jointly with and the square of , and when and . Find when and .

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    , so .

  12. 12.

    varies jointly with and . If is halved and is multiplied by 6, by what factor is multiplied?

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    .
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MPhil in Mathematics, Founder of Mathovia
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Joint Variation Practice Problems

These problems follow the joint variation lesson. Read each problem’s wording carefully: “jointly” multiplies, “inversely” divides.

The equations

Common mistakes to watch for

  • Treating it as direct variation in one variable. In , depends on both and ; find using all the given values at once.
  • Forgetting powers. If varies jointly with and the square of , the model is , not .
  • Using the wrong data to find . Find from the first complete set of values, then substitute the new values into the same equation.
  • Mixing joint and inverse variation. In “varies jointly with and inversely with ”, goes in the denominator: .

Frequently Asked Questions

How do I find k?+

Substitute the given values into the equation, such as y = kxz, and solve for k.

What is combined variation?+

A mix of direct and inverse variation, such as y = kx/z: y rises with x and falls as z rises.

More practice problems

Direct Variation Practice Problems Inverse Variation Practice Problems Algebra Word Problems Practice